RU2096818C1 - Method determining poisson's ratio of mobile object and device for its realization - Google Patents

Abstract

FIELD: magnetic prospecting for mineral resources, cosmic studies for measurement of magnetic field of terrestrial space and magnetic fields of planets, magnetic navigation for location of ships, etc. SUBSTANCE: method determining Poisson's ratio of mobile object lies in charge of at least two out of three angles of course, roll and pitch of object with respect to reference coordinate system and in measurement of method angles of projections in process of change of nine vectors of magnetic induction in coordinate system of object, in measurement of angles of course, roll and pitch of object and in determination of direction cosines of each axis of coordinate system of object in reference coordinate system by them, in measurement of projections of vectors of magnetic induction is step with measurement of angles of course, roll and pitch at which direction cosines of axes of coordinate system of object are different during each measurement of mentioned projections, in additional measurement of change of two out of three angles of course, roll and pitch of object as minimum and during angular positioning of axes of coordinate system of object differing from previous ones, in measurement of projections of tenth vector of magnetic induction and direction cosines of each axis of coordinate system of object and in determination of Poisson's ratios corresponding to vectors of magnetic induction and of direction cosines of coordinate axes of coordinate system of object by measured projections of vectors of magnetic induction. Device for realization of method incorporates three-component magneto-sensitive transducer rigidly coupled to object, three amplification-conversion units, generator of variable emf, angle measuring gear, recorder and information processor. EFFECT: increased authenticity of determination of Poisson's ratios. 2 cl, 2 dwg

Description

 The present invention relates to the field of measurement technology and can be used in magnetic exploration for mineral exploration, in the field of space research for measuring the magnetic field of near-Earth space and the magnetic field of planets, in magnetic navigation to determine the location of a vessel, etc.

There is a method of determining the Poisson's ratio of a moving object and a device for its implementation (Lysenko A.P. Theory and methods of compensating magnetic interference // Collection of articles "Geophysical instrumentation". L. Mingeology and mineral resources of the USSR. Design Bureau. 1960, issue 7, p. 44 58). The method consists in measuring the magnitude of the magnetic induction vector using a modular sensor, in particular a quantum sensor with periodic transverse rolls of a moving object at four main magnetic courses, respectively 0 ^o , 90 ^o , 180 ^o , 270 ^o , then measuring the magnitude of the magnetic induction vector periodic longitudinal rolls of a moving object at the four main courses mentioned and the measured magnetic field parameters at the main four courses of the object when passing over a landmark known to and the module of the magnetic induction vector of the geomagnetic field in the area of displacement of the object is determined from nine Poisson's coefficients, which can be represented as a tensor of magnetic masses of soft iron (Guzeev S.T. Semevsky RB.Determination of Poisson's parameters from measurements of magnetic induction by a T-magnetometer // Geophysical equipment. L. Nedra, 1980, issue 70, pp. 25-30).

две разности (a k), (e k), три суммы (b + d), (c + q), (f + h), а также составляющие постоянного магнитного поля подвижного объекта, при этом магнитный курс, поперечные и продольные углы кренов определяют соответственно от магнитного компаса и гировертикали, значение модуля вектора магнитной индукции геомагнитного поля определяют, например, по показаниям аэромагнитометра, а наклонение по магнитным картам (Лысенко А.П. Теория и методы компенсации магнитных помех // Сб. статей "Геофизическое приборостроение". Л. Мингеологии и охраны недр СССР. ОКБ, 1960, вып.7, с.54, абз.1, с.56, абз.4). Известное решение обеспечивает только определение двух разностей и трех сумм коэффициентов Пуассона. В известном техническом решении попарное определение коэффициентов Пуассона (a k), (e k), (b + d), (c + q), (f + h) осуществляется при малых кренах объекта, равных примерно 10^o, принимая при этом косинусы таких углов равными единице, а синусы этих углов равными соответствующим углам, выраженным в радианах, что снижает точность определения попарных значений коэффициентов Пуассона.

two differences (ak), (ek), three sums (b + d), (c + q), (f + h), as well as the components of the constant magnetic field of a moving object, while the magnetic course, the transverse and longitudinal angles of the rolls determine respectively, from the magnetic compass and the gyrovertical, the magnitude of the magnetic induction vector of the geomagnetic field is determined, for example, by the readings of an aeromagnetometer, and the inclination by magnetic maps (Lysenko A.P. Theory and methods of compensating magnetic interference // Collection of articles "Geophysical Instrumentation". L Mingeology and protection of the bowels of the USSR. OKB, 1960, issue 7, p.5 4, para. 1, p. 56, para. 4). The known solution provides only the determination of two differences and three sums of Poisson's ratios. In the known technical solution, the pairwise determination of the Poisson's ratios (ak), (ek), (b + d), (c + q), (f + h) is carried out for small rolls of the object equal to about 10 ^o , taking the cosines of such angles equal to unity, and the sines of these angles equal to the corresponding angles expressed in radians, which reduces the accuracy of determining the pairwise values of the Poisson's ratios.

 In the known method and device for determining the sums and differences of Poisson's ratios, it is necessary to have an inclination value, which is determined by magnetic cards. But the magnetic field changes in time, each of its changes is determined by the results of measurements in all magnetic observatories of the world, as well as with a satellite. Maps of the elements of the earth's magnetic field are compiled by the IZMIR RAS every five years and refer to the middle of the year, a multiple of five (Logachev A.A. Zakharov V.P. Magnetic prospecting. L. Nedra, 1979, p.16, 17). A change in the Earth's magnetic field causes a change in inclination, which leads to a decrease in the accuracy of determining the sums and differences of Poisson's ratios.

In addition, all the calculation formulas for determining the Poisson's ratios were derived under the assumption that the movement of a real object, in particular an airplane, a ship, is carried out strictly at four main courses, respectively equal to 0 ^o , 90 ^o , 180 ^o , 270 ^o , and periodic rolls are performed one type (transverse, and then longitudinal) with the same amplitude of vibrations. However, in the real motion of an object, this condition is not feasible, since rotation about any of the object’s axes causes additional (parasitic) rotations relative to the other two axes, and these parasitic evolutions during movement can only be partially reduced (Reznik E.E. Kantorovich V.L. Some issues of compensation of the aircraft’s magnetic fields // Collection of articles "Geophysical Instrumentation". L. Nedra, 1964, issue 18, p. 26 30).

где X_ix a k; X_iy b + d; Z_ix c + q; Y_iy e k; Z_iy f + h; X_p, Y_p, Z_p - проекции вектора магнитной индукции постоянного магнитного поля объекта.There is a method of determining the Poisson's ratios (Reznik EE Kantorovich V. L. Some issues of compensation of the magnetic fields of the aircraft // Collection of articles "Geophysical instrumentation". L. Nedra, 1984, issue 18, p. 34 36), which the set of essential features is closest to the proposed and adopted as a prototype. The known method consists in changing the angles of the heading, roll, pitch of a moving object, measuring in the process of changing the mentioned angles of nine modules and nine values of each projection of the magnetic induction vectors on the axis of the object’s coordinate system, which are different from each other, measuring, for example, without distorted ground stationary magnetometers object of the module of the vector of magnetic induction of the geomagnetic field from magnetic cards, and then from the measured parameters of the magnetic field to determine two differences and three sums of Poiss coefficients at respectively equal (ak), (ek), (b + d), (c + q), (f + h), and determining the vector components of the magnetic induction of constant magnetic field object. From the measured nine values of the modules of the magnetic induction vectors T ₁ , T ₂ , T _{9, the} value of the magnetic induction vector of the geomagnetic field T is taken and nine values of the differences of the modules of the magnetic induction vectors ΔT ₁ = T ₁ -T, ΔT ₂ = T ₂ -T, are obtained. .., ΔT ₉ = T ₉ -T. After that, the following is subtracted from each previous difference in the magnitude of the modules of the magnetic induction vectors, obtaining eight values of ΔT _i -ΔT _{i + 1} where i 1, 2, 3, and a system of eight equations, which can be represented in the following general form (Reznik E.E. Kantorovich VL Some issues of compensation of the magnetic fields of an airplane // Collection of articles "geophysical instrumentation". L. Nedra, 1964, issue 18, p. 35):

where X _ix ak; X _iy b + d; Z _ix c + q; Y _iy ek; Z _iy f + h; X _p , Y _p , Z _p - projection of the magnetic induction vector of the constant magnetic field of the object.

The known method, like the analogue, provides the determination of only two differences and three sums of Poisson's ratios. In the known technical solution of the projection of the magnetic induction vector X _i , Y _i , Z _i , X _{i + 1} , Y _{i + 1} , Z _{i + 1 is} measured on a moving object. Therefore, the value of each of these projections is the sum of the projections of the magnetic induction vectors of the geomagnetic field and the magnetic field of the moving object. However, the mentioned projections enter into the calculation formulas as projections of the magnetic induction vector of only the geomagnetic field (Reznik E. E. Kantorovich VL Some issues of compensation of the aircraft magnetic fields // Collection of articles "Geophysical Instrumentation". L. Nedra, 1964, no. 18, p. 34, para 1 below, p. 35), which leads to an error in determining the Poisson's ratios, and, consequently, to a decrease in the accuracy of determining these coefficients.

 In the known method, nine different values of the projections of the magnetic induction vectors are measured in the process of changing the course angles, roll, pitch. Different values of the ratios of the projections of the magnetic induction vectors to the geomagnetic field may not correspond to the values of the directing cosines of the axes of the coordinate system of the object relative to the magnetic induction vector of the geomagnetic field, since the projections are equal to the sum of the projections of the geomagnetic field and the magnetic field of the object, and the direction cosines of the axes of the coordinate system of the object are functions of inclination and course angles, roll, pitch of the object. Therefore, the solution of the above system of eight equations may be unstable, which reduces the accuracy of determining the Poisson's ratios.

 In the known method, as well as in the analogue, to determine the Poisson’s coefficients, it is necessary to know the spatial distribution of the module of the magnetic induction vector of the geomagnetic field in the region of motion of the object or the value of the undistorted object of the module of the vector of magnetic induction of the geomagnetic field over well-identifiable landmarks where the object is evolved to determine the Poisson's ratios (Logachev A.A. Zakharov V.P. Magnetic prospecting. L. Nedra, 1979, p. 105, 106; Vatsuro A.E. Tsirel V.S. Measurement and compensation of magnetic interference in aircraft that AN-2. Principles and methods) // Geophysical equipment L. Nedra, 1979, issue. 69, p. one hundred). Therefore, to determine the Poisson's ratios of a moving object by known methods, a piece of space should be prepared for a moving object with known parameters of the natural (undistorted by the object) magnetic field. Therefore, the known methods do not provide the ability to determine the Poisson's ratios under operating conditions, in particular, in magnetic recording conditions.

 Known technical solutions for measuring projections of the vector of magnetic induction (Afanasyev Yu.V. Fluxgate devices. L. Energoatomizdat, 1986, p. 117) and the module of the vector of magnetic induction (Logachev A.A. Zakharov V.P. Magnetic prospecting. L. Nedra, 1979, p. 85 94), which together represent a device for implementing a method for determining Poisson's ratios. The device contains a modular magnetosensitive sensor, a measuring and recording unit, the input of which is connected to the inputs of the said sensor, a three-component magnetosensitive sensor, three amplifier-converter blocks, the first inputs of which are connected to the outputs of the three-component sensor, and the first outputs to the inputs of this sensor, a variable emf generator, the outputs of which are connected to the input of a three-component sensor and the second inputs of the amplifier-conversion blocks, and a recording unit, the inputs of which are connected They are connected to the outputs of the amplifier-converter blocks and to the third output of the measuring and recording unit, which consists of a high-frequency generator, a phase shifter, and a variable-frequency voltage amplifier. Three-component and modular sensors are rigidly connected to a moving object.

 The known device operates as follows. The voltage from the high-frequency generator of the measuring and recording unit supplied to the input of the modular sensor polarizes the working substance, for example, cesium vapor of the sensor. As a result of this, the voltage of the useful signal with the precession frequency of the magnetization vector of the working substance around the vector of the external magnetic field appears at the output of the sensor, while the precession frequency is equal to the product of the gyromagnetic ratio of the core of the atom of the working substance to the external magnetic field module. This voltage is amplified by a variable frequency amplifier of the measuring and recording unit and from one of the outputs of this amplifier is fed to the recording unit (frequency meter), and from the second output to the phase shifter of the measuring and recording unit, the output signal from which is fed to the input of the modular sensor, providing positive feedback . Thanks to the positive feedback, a self-oscillating system is created that generates at a resonant frequency proportional to the external magnetic field. At the first input of a three-component sensor, the voltage exciting this sensor is supplied from a variable EMF generator. As a result of this, three emfs of the second harmonic appear at the outputs of the three-component sensor, each of which is proportional to the projection of the magnetic induction vector onto the corresponding magnetic axis of the three-component sensor (Afanasyev Yu.V. Ferrozond devices. L. Energoatomizdat, 1986, p. 66). The output signals from the three-component sensor are amplified and detected in the corresponding amplifier-conversion units. To detect the signals, the second inputs of the amplifier-converter blocks are supplied with alternating voltage from a variable emf generator. The output signal from each amplifier-converter unit is fed to a recording unit, which provides synchronous registration of the values of the projections of the magnetic induction vectors and the modules of the magnetic induction vectors when changing the course angles, roll, pitch of the moving object. From the measured values of the modules and projections of the magnetic induction vectors when the angular position of the moving object changes, from the value of the undistorted object to the module of the magnetic induction vector of the geomagnetic field, measured, for example, by a stationary ground magnetometer at the location of the recognized landmark, two differences and three sums of Poisson's ratios are determined, respectively equal to (ak), (ek), (b + d), (f + h), (c + q).

 Thus, the known device provides the determination of two differences and three sums of Poisson's ratios. The output signals from the amplifier-converting units of the known device located on a moving object are proportional to both the projections of the magnetic induction vector of the geomagnetic field and the projections of the magnetic induction of the magnetic field of the moving object. However, the mentioned output signals enter into the calculation formulas as projections of the magnetic induction vector of only the geomagnetic field (Reznik E.E. Kantorovich V.L. Some problems of compensation of the aircraft magnetic fields // Collection of articles "Geophysical Instrumentation". L. Nedra, 1964, no. . 18, p. 34, para. 1 below, p. 35), which leads to a decrease in the accuracy of determination of pairwise sums and differences of Poisson's ratios.

 To determine the Poisson coefficients by a known device, it is necessary to know the spatial distribution of the geomagnetic field magnetic induction vector module not distorted by the object in the region of the object’s motion or the value of the geomagnetic field magnetic induction vector module not distorted by the object over an identifiable landmark where the object is evolved to determine the Poisson coefficients. Therefore, in order to determine the Poisson's ratios of a moving object by a known device, a piece of space (stand) with known parameters of the geomagnetic field must be prepared, therefore, the said device does not provide the ability to determine the Poisson's ratios in operating conditions, for example, in magnetic recording conditions.

 In addition, from the totality of the measurements made in the known technical solutions, it is possible to determine pairwise values of two differences and three sums of Poisson's ratios only using approximate formulas, assuming that the modulus of the magnetic induction vector of the geomagnetic field is much larger than the modulus of the magnetic induction vector of a moving object (Vatsuro A.E. Tsirel V. S. Measurement and compensation of magnetic interference of the AN-2 aircraft (Principles and methods) //. Geophysical equipment. L. Nedra, 1979, issue 69, p. 98). However, for a number of objects, in particular, for ships with a displacement of 2 to 7 thousand tons, only the inductive magnetic field can reach up to 10,000 nT (Guzeev S.T. Semenovsky RB.Determination of Poisson parameters from measurements of magnetic induction by a T-magnetometer // Geophysical equipment. L. Nedra, 1980, issue 70, p. 25, para. 2). The measurement range of the module of the full vector of the magnetic induction of the geomagnetic field is from 33,000 nT to 66,000 nT (Logachev A.A. Zakharov V.P. Magnetic prospecting. L. Nedra, 1979, p. 14, paragraph 1 below). The determination of paired values of the Poisson's ratios using approximate calculation formulas for moving objects whose magnetic field differs from the geomagnetic field by less than an order of magnitude leads to a decrease in the accuracy of determination of the mentioned coefficients.

 The objective of the invention is to develop a method for determining all nine Poisson's ratios of a moving object and a device for its implementation, while the determination of Poisson's ratios should be carried out not only on specially made stands with a known module of the geomagnetic field vector, but also under operating conditions, in particular under magnetic shooting when there is no information about the value of the external magnetic field, for example, the magnetic field of the Earth, not distorted by a moving object. The problem is solved by measuring the resulting values of the projections of the magnetic induction vector of the external field (Earth's magnetic field) in the coordinate system of the moving object and the projections of the magnetic induction vectors of the inductive and constant fields of the object in the same coordinate system during the evolution of the mentioned object (when changing at least two from the three angles of the course, roll, pitch of the object), as in the absence of this information, but having information about the Poisson's ratios of the sample made of soft magnetically iron.

 The proposed technical solution consists of two methods and two devices for implementing these methods, so interconnected that they form a single common inventive concept.

 The proposed method for determining the Poisson's ratios of a moving object at a point in space, rigidly connected with the coordinate system of the object (according to the first option), consists in measuring the magnetic induction vector module in the selected location in the absence of a moving object, placing the moving object in the space, and changing course roll, pitch of the object relative to the reference coordinate system, measurement in the process of changing the mentioned projection angles of the magnetic induction vectors on the axis of the coordinate system object datum and calculation of Poisson's ratios, using measured values of the modulus and projections of nine magnetic induction vectors, changing at least two of the three angles of the heading, roll, pitch of the object, measuring the heading angles, roll, pitch of the object and using them to determine the direction cosines of each axis of the system the coordinates of the object in the reference coordinate system, and the projections of the magnetic induction vectors are measured synchronously with the measurement of the course, roll, pitch angles, the choice of the projections of ten magnetic induction vectors, at which I direct the cosines of the axes of the coordinate system of the object are different for each measurement of the projections mentioned, and for determining the Poisson ratios from the measured modulus of the magnetic induction vector in the absence of the object and the projections of ten magnetic induction vectors defined as functions of the guiding cosines of the measured heading, roll, pitch and unknown parameters, which are the projections of magnetic induction on the axis of the reference coordinate system in the absence of an object, a constant magnetic field of the object and Poisson's ratios of the object.

 The proposed method for determining the Poisson's ratios of a moving object at a point in space that is rigidly connected with the coordinate system of the object (according to the second option) consists in changing the angles of the course, roll, pitch of the object relative to the reference coordinate system, measuring in the process of changing the mentioned projection angles of the magnetic induction vectors on the axis the coordinate system of the object and the calculation of Poisson's ratios, using the measured values of the projections of nine vectors of magnetic induction, changing at least two of the three angles the course, roll, pitch of the object and from them the determination of the directional cosines of each axis of the coordinate system of the object in the reference coordinate system, and the projections of the magnetic induction vectors are measured synchronously with the measurement of the course, roll, pitch angles, the choice of the projections of ten magnetic induction vectors for which the direction cosines the axes of the object’s coordinate system are different for each measurement of the mentioned projections, then at an additional point in space that is rigidly connected with the object’s coordinate system, placing the sample from soft to magnesium in relation to iron, whose Poisson's ratios are known at the main point in space, again changing at least two of the three angles of the heading, roll, pitch of the object, measuring the heading angles, roll, pitch of the object and using them determine the direction cosines of each axis of the coordinate system of the object in the reference coordinate system, and the projections of the magnetic induction vectors are measured simultaneously with the measurement of the course, roll, pitch angles, the choice of the projections of ten magnetic induction vectors on at least one of the same axis of the object, at which The apparent cosines are different for each measurement of the projections mentioned, and for determining the Poisson's ratios of the object from the projections of ten magnetic induction vectors in the absence of a sample, defined as functions of the measured heading angles, roll, pitch and unknown parameters, which are the magnetic induction projections on the axis of the reference coordinate system for the absence of the object, the constant magnetic field of the object, the Poisson's ratio of the object and the projections of ten vectors of magnetic induction on at least one of the same axis of the systems s the coordinates of the object in the presence of the sample, defined as functions of the guiding cosines of the measured heading angles, roll and pitch, the known Poisson's ratios of the sample and unknown parameters, which are the projections of magnetic induction on the axis of the reference coordinate system in the absence of the object and the sample, the constant magnetic field of the object and sample and Poisson's ratios of the object.

 A change in the present invention (according to the method of the first and second variants) of at least two of the three angles of the course, roll, pitch of the moving object leads to a change in the projections of the magnetic field vector of the external field, for example, the Earth’s magnetic field (magnetic field), and a change in the magnetic induction vector of the aforementioned of the object on the coordinate axis of the object is proportional to the direction cosines of each axis of the coordinate system of the object relative to the reference coordinate system, while the inductive field of the object is a function of the Poisson's ratios the object and the vector of the external magnetic field, in particular, the MPZ. When synchronously measuring the projections of ten vectors of magnetic induction with measuring the varying angles of the course, roll, pitch of the object, at which the direction cosines of the axes of the coordinate system of the object are different, ten values of each projection of the vector of magnetic induction on the axis of the coordinate system of the object are obtained. The value of each of the measured projections of the magnetic induction vectors can be set analytically in the form of functions of the guiding cosines of the measured heading angles, roll, pitch of the object, unknown values of the projections of the magnetic induction vectors of the magnetic field, the constant magnetic field of the object, and the Poisson's ratios of the object. Thus, we obtain a system of ten equations for the mentioned values of the projections onto the same coordinate axis of the object.

 For the method according to the first embodiment, the general solution of the obtained equations for the measured module of the magnetic induction vector in the absence of an object in the selected space location is nine Poisson's ratios of the object, the projection of the magnetic induction vector of the external magnetic field, in particular, the magnetic field, projections of the constant and inductive fields of the object.

 For the method according to the second embodiment, placing at an additional point in space, rigidly connected with the coordinate system of the object, a sample of magnetically soft iron, the Poisson ratios of which are known at the main point in space, and then changing at least two of the three course angles, heel, pitch of a moving object leads to a change in the projections of the magnetic induction vector of the external field, for example, the magnetic field, and to a change in the magnetic induction vector of the inductive field of the object and the sample in proportion to the guides of the cosine each axis of the object’s coordinate system relative to the reference coordinate system itself, while the inductive field of the object is a function of the Poisson’s coefficients of the object and the sample, the vector of the external magnetic field, in particular the magnetic field. When synchronously measuring the projections of ten magnetic induction vectors with measuring the angles of the heading, roll, and pitch of the object, at which the guiding axes of the axes of the object’s coordinate system are different, ten values of each projection of the magnetic induction vector on the axis of the object’s coordinate system are obtained. The value of each of the measured projections of the magnetic induction vectors can be set analytically in the form of the guiding cosines of the measured heading angles, roll, pitch of the object, known Poisson coefficients of the sample and unknown projections of the magnetic field vectors of the constant magnetic field of the object and the sample and Poisson's ratios of the object. Thus, we obtain for the mentioned values of projections onto the same coordinate axis of the object an additional system of ten equations in the presence of a sample. The general solution obtained in the presence of the sample and previously obtained equations in the absence of the sample are nine Poisson's ratios of the object, the projection of the magnetic induction vector of the external magnetic field, in particular the magnetic field, the constant and inductive fields of the object and the sample.

 Thus, the technical result of the proposed method is expressed in the determination of all nine Poisson's ratios of a moving object both in the presence of information about the value of the magnetic field not distorted by the object (for the method according to the first embodiment), and in the absence of information (for the method according to the second embodiment) about the value external magnetic field, not distorted by the magnetic field of the object, while the totality of the results of the measured parameters provides the determination of the Poisson's ratios of the object not by approximate but by exact forms ulam.

The proposed device (according to the first embodiment) for implementing the method of determining the Poisson's ratios of a moving object at a point in space, rigidly connected with the coordinate system of the object, containing a three-component magnetosensitive sensor located at the said point in space, three amplifier-converter blocks, the first inputs of which are connected to the outputs of the aforementioned sensor, variable EMF generator, the first output of which is connected to the input of a three-component sensor, and the second output to the second inputs of the amplifier of the conversion units, and the recording unit, the inputs of which are connected to the outputs of the amplification-conversion units, is equipped with an angle measuring device, the outputs of which are connected to three additional inputs of the recording unit, which is capable of synchronously recording signals proportional to the values of the projections of the magnetic induction vectors and course angles, roll, pitch of the object, and an information processing device connected to the output of the recording unit, with the possibility of calculating the coefficients P wasson from the following system of equations:
B _xi = l _1i (1 + a) • B _xt + m _1i (1 + a) • B _yt + n _1i (1 + a) • B _zt + b (l _2i B _xt + m _2i B _yt + n _2i B _zt + c (l _3i (B _xt + m _3i B _yt + n _3i B _zt ) + B _xp ;
B _yi = l _2i (1 + e) • B _xt + m _2i (1 + e) • B _yt + n _2i (1 + e) • B _zt + d (l _1i B _xt + m _1i B _yt + n _1i B _zt ) + f (l _3i B _xt + m _3i B _yt + n _3i B _zt ) + B _yp ;
B _zi = l _3i (1 + k) • B _xt + m _3i (1 + k) • B _yt + n _3i (1 + k) • B _zt + q (l _1i B _xt + m _1i B _yt + n _1i B _zt + h (l _2i B _xt + m _2i B _yt + n _2i B _zt ) + B _zp ,
where B _xi , B _yi , B _{zi are the} projections of the magnetic induction vectors on the axis of the coordinate system of the object at ix values of the angles of the course, roll, pitch of the object;
i = 1, 2, 10;
B _xt , B _yt , B _zt projections of the magnetic induction vector on the axis of the reference coordinate system in the absence of an object;
l _1i , m _1i , n _1i , l _2i , m _2i , n _2i , l _3i , m _3i , n _{3i the} direction cosines of the axes of the coordinate system of the object with ix values of the course angles, roll, pitch of the object;
B _xp , B _yp , B _zp projections of the magnetic induction vector on the axis of the coordinate system of the object, created by the magnetically hard iron of the object;
a, b, c, d, e, f, q, h, k Poisson's ratios of the object at the point of the sensor placement space.

The proposed device (according to the second embodiment) for implementing the method of determining the Poisson's ratios of a moving object at a point in space, rigidly connected with the coordinate system of the object, containing a three-component magnetosensitive sensor located at the said point in space, three amplifier-conversion blocks, the first inputs of which are connected to the outputs of the aforementioned sensor, variable EMF generator, the first output of which is connected to the input of a three-component sensor, and the second output to the second inputs of the amplifier but-converter blocks, and the recording block, the inputs of which are connected to the outputs of the amplifier-conversion blocks, is equipped with an angle measuring device, the outputs of which are connected to three additional inputs of the recording block, configured to synchronously register signals proportional to the values of the projections of the magnetic induction vectors and course angles, roll, pitch of the object, a sample of magnetically soft iron with the possibility of its placement at an additional point in space, rigidly with knitted with the coordinate system of the object, and the information processing device connected to the output of the recording unit, with the possibility of calculating the Poisson's ratios from the following system of equations:
B _xi = l _1i (1 + a) • B _xt + m _1i (1 + a) • B _yt + n _1i (1 + a) • B _zt + b (l _2i B _xt + m _2i B _yt + n _2i B _zt + c (l _3i B _xt + m _3i B _yt + n _3i B _zt ) + B _xp ;
B _yi = l _2i (1 + e) • B _xt + m _2i (1 + e) • B _yt + n _2i (1 + e) • B _zt + d (l _1i B _xt + m _1i B _yt + n _1i B _zt ) + f (l _3i B _xt + m _3i B _yt + n _3i B _zt ) + B _yp ;
B _zi = l _3i (1 + k) • B _xt + m _3i (1 + k) • B _yt + n _3i (1 + k) • B _zt + q (l _1i B _xt + m _1i B _yt + n _1i B _zt + h (l _2i B _xt + m _2i B _yt + n _2i B _zt ) + B _zp ;
B _xj = l _1j (1 + a + a ₀ ) • B _xt + m _1j (1 + a + a ₀ ) • B _yt + n _1j (1 + a + a ₀ ) • B _zt + (b + b ₀ ) • (l _2j B _xt + m _2j B _yt + n _2j B _zt + (c + c ₀ ) • (l _3j B _xt + m _3j B _yt + n _3j B _zt ) + B _xp + B _x0 ; B _yj = l _2i (1 + e + e ₀ ) • B _xt + m _2j (1 + e + e ₀ ) • B _yt + n _2j (1 + e + e ₀ ) • B _zt + (d + d ₀ ) • (l _1j B _xt + m _1j B _yt + n _1j B _zt + (f + f ₀ ) • (l _3j B _xt + m _3j B _yt + n _3j B _zt ) + B _yp + B _y0 ;
B _zj = l _3j (1 + k + k ₀ ) • B _xt + m _3j (1 + k + k ₀ ) • B _yt + n _3j (1 + k + k ₀ ) • B _zt + (q + q ₀ ) • (l _1j B _xt + m _1j B _yt + n _1j B _zt + (h + h ₀ ) • (l _2j B _xt + m _2j B _yt + n _2j B _zt ) + B _zp + B _zo , where B _xi , B _yi , B _zi , B _xj , B _yj , B _zj projections of the magnetic induction vectors on the axis of the coordinate system of the object with ix and jx values of the course angles, roll, pitch of the object with and without a sample;
i = 1, 2, 10; j = 1, 2, 10;
B _xt , B _yt , B _zt projections of the magnetic induction vector on the axis of the reference coordinate system in the absence of an object;
l _1i , m _1i , n _1i , l _2i , m _2i , n _2i , l _3i , m _3i , n _3i and l _1j , m _1j , n _1j , l _2j , m _2j , n _2j , l _3j , m _3j , n _{3j are the} directing cosines of the axes of the object's coordinate system at ix and jx values of the course angles, roll, pitch of the object;
B _xp , B _yp , B _zp , B _x0 , B _y0 , B _z0 - projections of the magnetic induction vector on the axis of the coordinate system of the object, created by the magnetically hard iron of the object and the sample;
a, b, c, d, e, f, q, h, k and a ₀ , b ₀ , c ₀ , d ₀ , e ₀ , f ₀ , q ₀ , h ₀ , k ₀ Poisson's ratios of the object and the sample in point of the sensor placement space, while the Poisson's ratios of the sample located at an additional point in space are known at the location of the three-component sensor.

 The set of tools used for the device according to the first embodiment, one of which is designed to measure the projections of the magnetic induction vector, consisting of a three-component sensor, rigidly connected to a moving object, three amplifier-converter blocks and a variable emf generator, the second for measuring heading angles, roll, pitch an object, not magnetic physical quantities, and a third for simultaneously registering the projections of the magnetic induction vectors and the mentioned angles of the object and the device for processing this information, form a single device that provides the determination of nine Poisson's ratios of the object from the synchronously measured projections of the magnetic induction vectors, each of which is equal to the sum of the magnetic induction vectors of the magnetic field and the magnetic field of the object, with the measurement of the changing course angles, roll, pitch of the object and information about the magnetic induction module of the magnetic field stand at which measurements are taken.

 The set of tools used for the device according to the second embodiment, one of which is designed to measure the projections of the magnetic induction vector, consisting of a three-component sensor, rigidly connected to a moving object, three amplifier-converter blocks and a variable emf generator, the second for measuring heading angles, roll, pitch an object, and not magnetic physical quantities, the third for simultaneously recording the projections of the magnetic induction vectors and the mentioned angles of the object and the information processing device and four The fourth one consisting of a sample of magnetically soft iron, with the possibility of its placement at an additional point in space, the Poisson ratios of which are known at the location of the sensor, form a single device that provides synchronously measured projections of the magnetic induction vectors in the absence of a sample at an additional point in space , with the measurement of changing course angles, roll, pitch of the object, determination of nine Poisson's ratios of the object at the location of the sensor.

 Thus, the technical result of the proposed device is expressed in the determination of all nine Poisson's ratios of the moving object, both in the presence of information about the module of the magnetic induction vector of the external magnetic field, in particular, the magnetic field, not distorted by the magnetic field of the object (for the device according to the first embodiment), and in the absence this information (for the device according to the second embodiment), which allows the determination of Poisson's ratios under operating conditions, for example, in magnetic recording conditions.

 The essence of the proposed method and device for its implementation is illustrated by the following graphic materials.

 In FIG. 1 shows a block diagram of a device for implementing the method for determining the Poisson's ratios of an object.

 In FIG. 2 shows the directions of the axes of the object in the reference coordinate system at the corners of the course, roll, pitch.

 The proposed device (according to the first embodiment) for implementing the method for determining the Poisson ratios of a moving object according to the first embodiment consists (see Fig. 1) of a three-component magnetosensitive sensor 1, three amplifier-converter blocks 2 4, the first inputs of which are connected to the outputs of the sensor 1, generator EMF variable 5, the first output of which is connected to the input of the sensor 1, and the second output to the second inputs of blocks 2 4, of the recording block 6, whose inputs are connected to the outputs of blocks 2 - 4, of the angle measuring device 7, the outputs of which are connected to three additional inputs of block 6, and the information processing device 8, connected to the output of block 6. In this case, the sensor 1, blocks 2 4, generator 5, block 6, device 7 and block 8 are located on the movable object 9.

 The claimed method according to the first embodiment is implemented by the proposed device (according to the first embodiment) as follows.

At the first input of a three-component sensor 1 (see Fig. 1), in particular a flux gate, an EMF variable is supplied from the generator 5, exciting this sensor. As a result of this, three emfs of the second harmonic appear at the output of sensor 1, each of which is proportional to the projection of the magnetic induction vector onto the corresponding magnetic axis of sensor 1 (Afanasyev Yu.V. Ferrozond devices. L. Energoatomizdat, 1986, p. 66). The output signals from the sensor 1 are amplified and detected in the corresponding blocks 2 -4. To detect the signals, the second inputs of blocks 2 4 are supplied with alternating voltage from the generator 5. The inputs from block 6 receive the signals from the outputs of blocks 2 4 proportional to the projections of the magnetic induction vectors, and the output signals from the device 7 proportional to the angles of the heading, roll, pitch of object 9 Block 6 provides synchronous registration of signals proportional to the values of the projections of the magnetic induction vectors and the angles of the course, roll, pitch of the object, and transfer them to the information processing device 8, when mod data is entered into it In the absence of an object, the magnetic induction vector of the external magnetic field is used to determine the Poisson's ratios and the components of the magnetic field of the object. When synchronously measuring the projections of ten vectors of magnetic induction and heading, roll and pitch angles, for example, during circulation of an object at which the direction cosines of the axes of the coordinate system of the object are different, ten values of the projections of the magnetic induction vectors B _xi , B _yi , B _zi per one and the same axis of the object. Algebraic expressions B _xi , B _yi , B _zi , forming a system of equations, are presented earlier in the proposed device according to the first embodiment. In these equations (l _1i , m _1i , n _1i ), (l _2i , m _2i , n _2i ), (l _3i , m _3i , n _3i ) the direction cosines of the corresponding axes O'X ', O'Y', O 'Z' (see. FIG. 2) object O'X'Y'Z 'coordinate system, which are functions of the course angle ψ q _to roll and pitch _at θ relative to the reference OXYZ coordinate system. In these equations, the unknown parameters are B _xp , B _yp , B _zp and the products of B _xt , B _yt , B _zt and Poisson's ratios. The measured parameters are the direction cosines of the axes of the object's coordinate system and B _xi , B _yi , B _zi for the directional cosines of the axes of the object's coordinate system that are different from each other, so each of the systems of the above equations has a stable and unique solution. The solution to this system of equations is (1 + a) • B _xt , (1 + a) • B _yt , (1 + a) • B _zt , b • B _xt , b • B _yt , b • B _zt , d • B _xt , d • B _yt , d • B _zt , (1 + e) • B _xt ,
(1 + e) • B _yt , (1 + e) • B _zt , f • B _xt , f • B _yt , f • B _zt , q • B _xt , q • B _yt , q • B _zt , h • B _xt , h • B _yt , h • B _zp , (1 + k) • B _xt , (1 + k) • B _yt , (1 + k) • B _zt , B _xp , B _yp , B _zp .

Аналогично определяют (1+e)•B_t, (1+k)•B_t, b•B_t, c•B_t, d•B_t, f•B_t, q•B_t, h•B_t.According to the decisions determined

Similarly define (1 + e) • B _t , (1 + k) • B _t , b • B _t , c • B _t , d • B _t , f • B _t , q • B _t , h • B _t .

By measuring, for example, a quantum magnetometer, the magnitude of the magnetic induction vector B _t , as presented in (Reznik E.E. Kantorovich V.L. Some problems of compensating the magnetic fields of an airplane // Collection of articles "Geophysical Instrumentation". L. Nedra, 1964 , issue 18, p. 26 30), in the absence of the influence of the magnetic field of the object and substituting its value in the obtained solutions of the product of the Poisson parameters by B _t , all nine Poisson parameters of the object 9 are determined at the location of the sensor 1, which is rigidly connected with the object 9.

The value of B _t can be determined by the geographic location of the object and magnetic field maps compiled and periodically adjusted by the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences (Logachev A.A. Zakharov V.P. Magnitorazvedka. L. Nedra, 1979).

 The proposed device (according to the second embodiment) for implementing the method for determining the Poisson ratios of a moving object according to the second embodiment consists (see Fig. 1) of a three-component magnetosensitive sensor 1, three amplifier-converter blocks 2 4, the first inputs of which are connected to the outputs of the sensor 1, generator EMF variable 5, the first output of which is connected to the input of the sensor 1, and the second output to the second inputs of blocks 2 4, of the recording block 6, whose inputs are connected to the outputs of blocks 2 - 4, of the angle measuring device 7, the outputs of which are connected to three additional inputs of block 6, an information processing device 8, connected to the output of block 6, and a sample 10 of magnetically soft iron with the possibility of its placement at an additional point in space, rigidly connected with the coordinate system of object 9. When this Poisson's ratio of the sample 10, located at an additional point in space, are known at the location of the sensor 1.

 The inventive method according to the second embodiment is implemented by the proposed device (according to the second embodiment) as follows.

The device according to the second embodiment, in the absence of sample 10 at an additional point (see Fig. 1), provides the determination of the product of the Poisson's ratios of the object by B _t similarly to the device according to the first embodiment, the values of which remain in the memory of device 8. Then, they are placed in an additional space point that is rigidly connected with the coordinate system of object 9, a sample 10 of magnetically soft iron, the Poisson parameters of which, when its orientation is selected, are known at the location of sensor 1. When synchronously measuring projections, syati vectors of magnetic induction and course angles, roll, pitch, for example, in the circulation of the object, in particular vessel in which the direction cosines of the axes of the object coordinate system are different, obtained ten values of the projections of the magnetic induction B _xj, B _yj, B _zj one and the same axis of the object. Algebraic expressions B _xj , B _yj , B _zj , forming a system of equations, are presented in the proposed device according to the second embodiment. In these equations (l _1j , m _1j , n _1j ), (l _2j , m _2j , n _2j ), (l _3j , m _3j , n _3j ) the direction cosines of the corresponding axes O'X ', O'Y', O 'Z' (see Fig. 2) of the coordinate system of the object O'X'Y'Z ', which are functions of the angles of the course ψ of the roll q _x and the pitch θ _y relative to the reference coordinate system OXYZ. In these equations, the unknown parameters are B _xp + B _x0 , B _yp + B _y0 , B _zp + B _z0 and the products B _xt , B _yt , B _zt and the corresponding sums of the Poisson's ratios of the object and the sample. The measured parameters are the direction cosines of the axes of the object's coordinate system, the Poisson's ratios of the sample and B _xj , B _yj , B _zj for the different directional cosines of the axes of the object's coordinate system, therefore, each of the systems of the mentioned equations has a stable and unique solution. The solution to this system of equations is (1 + a + a ₀ ) • B _xt , (1 + a + a ₀ ) • B _yt , (1 + a + a ₀ ) • B _zt , (b + b ₀ ) • B _xt , (b + b ₀ ) • B _yt , (b + b ₀ ) • B _zt , (c + c ₀ ) • B _xt , (c + c ₀ ) • B _yt , (c + c ₀ ) • B _zt , (d + d ₀ ) • B _xt , (d + d ₀ ) • B _yt , (d + d ₀ ) • B _zt , (1 + e + e ₀ ) • B _xt , (1 + e + e ₀ ) • B _yt , (1 + e + e ₀ ) • B _zt , (f + f ₀ ) • B _xt ,
(f + f ₀ ) • B _yt , (f + f ₀ ) • B _zt , (q + q ₀ ) • B _xt , (q + q ₀ ) • B _yt , (q + q ₀ ) • B _zt , (h + h ₀ ) • b _xt ,
(h + h ₀ ) • B _yt , (h + h ₀ ) • B _zp , (1 + k + k ₀ ) • B _xt , (1 + k + k ₀ ) • B _yt , (1 + k + k ₀ ) • B _zt , B _xp + B _x0 , B _yp + B _y0 , B _zp + B _z0 .

Аналогично определяют (1+e+e_o)•B_t, (1+k+k_o)•B_t, (b+b₀)•B_t, (c+c₀)•B_t, (d+d₀)•B_t, (f+f₀)•B_t, (q+q₀)•B_t, (h+h₀)•B_t.According to the decisions determined

Similarly determine (1 + e + e _o ) • B _t , (1 + k + k _o ) • B _t , (b + b ₀ ) • B _t , (c + c ₀ ) • B _t , (d + d ₀ ) • B _t , (f + f ₀ ) • B _t , (q + q ₀ ) • B _t , (h + h ₀ ) • B _t .

В месте расположения датчика 1 (см. фиг. 1) параметры Пуассона образца правильной геометрической формы, например в виде шара или эллипсоида, можно определить аналитически (Яновский Б.М. Земной магнетизм. Л. ЛГУ, 1978; Кожухов В. П. Воронов В.В. Григорьев В.В. Магнитные компасы. М. Транспорт, 1981) или экспериментально с помощью трехкомпонентной меры магнитной индукции (Афанасьев В.В. Студенов Н.В. Хорев В.Н. и др. Средства измерения параметров магнитного поля. Л. Энергия, 1979) в зависимости от изменения магнитной индукции внешнего намагничивающего поля, например, от изменения магнитной широты, при этом сохраняя неизменным взаимное расположение датчика и образца, которое они должны иметь при работе в полевых условиях.From the solution of the equations in the absence and presence of a sample, the Poisson parameters of the object and the values of B _xt , B _yt , B _{zt are} determined. So, for example, in the absence of sample 10, (1 + a) • B _t is determined, which is denoted by N ₁ , and in the presence of sample 10, (1 + a + a ₀ ) B _t is determined, which is denoted by N ₂ , that is, a system of two equations:
(1 + a) • B _t = N ₁
(1 + a + a ₀ ) • B _t = N ₂
The solution to this system will be

At the location of sensor 1 (see Fig. 1), the Poisson parameters of a sample of a regular geometric shape, for example, in the form of a ball or an ellipsoid, can be determined analytically (Yanovsky B.M. Earth magnetism. L. Leningrad State University, 1978; Kozhukhov V.P. Voronov VV Grigoryev VV Magnetic compasses. M. Transport, 1981) or experimentally using a three-component measure of magnetic induction (Afanasyev VV Studenov NV, Khorev VN and other means of measuring magnetic field parameters . L. Energia, 1979) depending on the change in the magnetic induction of the external magnetizing field, n example, by changes in the magnetic latitude while maintaining unchanged the mutual arrangement of the sensor and the sample, they must be in operation in the field.

 The technical solution according to the second option can be used to control the Poisson's ratios of the object and determine the zero offset of the teslameter or to adjust the constant and inductive magnetic field of the object under operating conditions, for example, in magnetic recording conditions.

 Thus, the technical result of the proposed technical solution is expressed in the determination of all nine Poisson's ratios of the object, both in the presence of information about the module of the magnetic induction vector of the external magnetic field, and in the absence of this information.

 In the proposed technical solution, the sensor 1 (see Fig. 1), blocks 2 4 and the generator 5 are made similar to the known device for measuring magnetic field parameters (Afanasyev Yu.V. Ferrozond devices. L. Energoatomizdat, 1986, p. 117). Moreover, each block 2 4 consists of a selective amplifier and a synchronous detector (Afanasyev Yu.V. Studentsov N.V. Shchelkin A.P. Magnetometric transducers, devices, installations. L. Energia, 1972, p. 155). The angle measuring device 7 (see Fig. 1) can be a gyrostabilized platform (GSP), which provides measurement of three angles of rotation of the object with an error of about 0.5 angular minutes due to the triaxial gyroscopic stabilization of the GSP relative to three mutually perpendicular axes of the reference coordinate system (Theory and Design gyroscopic instruments and systems // I.V. Odinova, G.D. Blumin, A.V. Karpukhin, and others M. Higher School, 1971, p. 387 -393, Fig. 9.9). For accurate measurement of the angular position of a moving object in a reference coordinate system with an error of up to tenths of arc seconds in the proposed technical solution, as a corner measuring device 7 (see Fig. 1), laser-based navigation systems can be used to measure heading angles, roll, pitch of gyroscopes with which airplanes are equipped (The tendency of improving gyroscopes and gyrostabilized platforms. D.P. Lukyanov, L.A. Severov, E.L. Smirnov, A.V. Til // L. Izv. Universities of the USSR. Instrument making. T. 30 , N 10, 1987). The recording unit 6 and the information processing device 8 can be implemented by the CPC (Universal Programmable Controller) developed and manufactured by IF-ATIS JSC (193131, St. Petersburg, 24 Ivanovskaya St., tel. (812) 568-37- 14, fax (812) 568-37-12).

 A sample of magnetically soft iron can be made of permalloy or Armco iron (V.P. Kozhukhov, V.V. Vorobiev, V.V. Grigoriev. Magnetic compasses. M. Transport, 1981).

Claims (2)

 1. The method of determining the Poisson's ratios of a moving object at a point in space that is rigidly connected with the coordinate system of the object, which consists in measuring the magnetic induction vector module in a selected place in space in the absence of a moving object, placing a moving object in the aforementioned space, changing the course, roll, pitch of the object relative to the reference coordinate system, measuring in the process of changing the mentioned projection angles of the magnetic induction vectors on the axis of the object coordinate system and calculating the coefficient Poisson ratios using the measured values of the modulus and projections of nine magnetic induction vectors, characterized in that at least two of the three angles of the heading, roll, pitch of the object are changed, the angles of the heading, roll, pitch of the object are measured and the directional cosines of each axis of the system are determined the coordinates of the object in the reference coordinate system, and the projections of the magnetic induction vectors are measured synchronously with the measurement of the angles of the course, roll, pitch, projections of ten magnetic induction vectors are chosen at which the direction cosines o the coordinate systems of the object are different for each measurement of the mentioned projections, and Poisson's ratios are determined from the measured modulus of the magnetic induction vector in the absence of the object and the projections of ten magnetic induction vectors defined as functions of the direction cosines of the measured heading, roll, pitch and unknown parameters, which are projections of magnetic induction on the axis of the reference coordinate system in the absence of an object, projections of a constant magnetic field of an object, and Poisson's ratios of the object. 2. A device for determining the Poisson's ratios of a moving object at a point in space, rigidly connected with the coordinate system of the object, containing a three-component magnetosensitive sensor located at said point in space, three amplifier-converter blocks, the first inputs of which are connected to the outputs of the said sensor, a variable emf generator, the first output of which is connected to the input of a three-component sensor, and the second output to the second inputs of the amplifier-converter blocks, and the recording unit, in the odes of which are connected to the outputs of the amplifier-conversion units, characterized in that it is equipped with an angle measuring device, the outputs of which are connected to three additional inputs of the recording unit, configured to synchronously register signals proportional to the values of the projections of the magnetic induction vectors and the course angles, roll, pitch of the object , and an information processing device connected to the output of the recording unit, with the possibility of calculating Poisson's ratios from the following system equalities:
B _{x i} l _{1 i} (1 + a) • B _{x t} + m _{1 i} (1 + a) • B _{y t} + n _{1 i} (1 + a) B _{z t} + b (l _{2 i} B _{x t} + m _{2 i} B _{y t} + n _{2 i} B _{z t} ) + c (l _{3 i} B _{x t} + m _{3 i} B _{y t} ) + n _{3 i} B _zt B _{x p} ; B _{y i} l _{2 i} (1 + l) B _{x t} + m _{2 i} (1 + l) B _{y t} + n _{2 i} (1 + e) B _{z t} + d (l _{1 i} B _{x t} + m _{1 i} B _{y t} + n _{1 i} B _{z t} ) + f (l _{3 i} B _{x t} + m _{3 i} B _{y t} + n _{3 i} B _{z t} ) + B _{y p} ;
B _{z i} l _{3 i} (1 + k) B _{x t} + m _{3 i} (1 + k) B _{y t} + n _{3 i} (1 + k) B _{z t} + g (l _{1 i} B _{x t} + m _{1 i} B _{y t} + n _{1 i} B _{z t} ) + h (l _{2 i} B _{x t} + m _{2 i} B _{y t} + n _{2 i} B _{z t} ) + B _{z p} ;

where B _{x i} , B _{y i} , B _{z i are the} projections of the magnetic induction vectors on the axis of the coordinate system of the object at the i-x values of the course angles, roll, pitch of the object; i 1,2,10;
B _{x t} , B _{y t} , B _{z t} projections of the magnetic induction vector on the axis of the reference coordinate system in the absence of an object;
l _{1 i} , m _{1 i} , n _{1 i} , l _{2 i} , m _{2 i} , n _2i , l _{3 i} , m _{3 i} , n _{3 i} directing cosines of the axes of the coordinate system of the object at i-x values of the course and roll angles, pitch of the object;
B _{x p} , B _{y p} , B _{z p} projections of the vector of magnetic induction on the axis of the coordinate system of the object, created by the magnetically hard iron of the object;
a, b, c, d, e, f, g, h, k Poisson's ratios of the object at the point of the sensor placement space.

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