RU2594057C1 - Method for uniaxial orientation of spacecraft with elongated shape - Google Patents

Abstract

FIELD: space.

SUBSTANCE: invention relates to controling spacecraft around its centre of gravity. Method includes turning spacecraft around its axis of minimum moment of inertia (longitudinal). Before turning, longitudinal axis of spacecraft is aligned with plane formed by normal to orbital plane and radius vector of spacecraft. Turning is performed until angle between longitudinal axis of spacecraft and orbital plane reaches a certain value depending on speed of turning and ratio of minimum moment of inertia of spacecraft to average value of transverse moments of inertia. Turning speed (order of orbital) is selected depending on specified angle and ratio of moments of inertia of spacecraft. Angle between radius-vector of spacecraft and vector directed from spacecraft centre of gravity towards centre of aerodynamic pressure of solar panels of spacecraft must not be more than 90°.

EFFECT: technical result of invention consists in implementing long-term mode of gravity orientation with spinning, with evolution of spacecraft rotation towards acceleration.

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Description

The invention relates to space technology and can be used to orient the spacecraft (SC) when performing experiments and research.

A known method of orientation of the spacecraft, including the exhibition of the axes of the spacecraft and maintaining the angular position of the spacecraft using orientation engines (Alekseev KB, Bebenin GG "Control of spacecraft", M .: Mashinostroenie, 1974).

However, to use this method, it is necessary to expend the working fluid, which, in addition, leads to contamination of the optical surfaces of the spacecraft and causes microacceleration on board the spacecraft.

A known method, including the exposure of the axis of the spacecraft, corresponding to the minimum moment of inertia, to the center of the earth and the orbital displacement of the spacecraft (Belyaev M.Yu. “Scientific experiments on spacecraft and orbital stations”, M .: Mashinostroenie, 1984). This method is used for spacecraft having an elongated shape, i.e. when the moment of inertia relative to the longitudinal axis is much less than the moment of inertia relative to the transverse axes.

In this case, the gravitational orientation of the spacecraft is of an elongated shape, which does not require maintaining the flow of the working fluid and, therefore, the optical surfaces of the spacecraft are not contaminated and do not cause acceleration due to the operation of orientation control engines.

However, due to an inaccurate exposure of the SC axis to the center of the Earth, angular velocities appear around all the SC axes. The presence of angular velocities around the transverse axes of the spacecraft leads to a deviation of the longitudinal axis of the spacecraft from the direction to the center of the earth, as a result of which the accuracy of the gravitational orientation of the spacecraft deteriorates.

, где I_yz - среднее значение близких по величине моментов инерции КА вокруг поперечных осей КА; I_х - момент инерции КА вокруг продольной оси; ω₀ - модуль абсолютной угловой скорости орбитальной системы координат.Closest to the proposed one is a method of uniaxial orientation of an extended spacecraft (RF Patent No. 2457159, priority date 08/30/2010, IPC (2006.01) B64G 1/34 - prototype), which includes setting the spacecraft axis corresponding to the minimum moment of inertia to the center of the earth and orbital spacecraft displacement, and after the spacecraft axis is set to the center of the Earth and the spacecraft’s orbital displacement, the spacecraft is twisted around the spacecraft axis set to the center of the Earth to the required moment with angular velocity

where I _yz is the average value of close in magnitude moments of inertia of the spacecraft around the transverse axes of the spacecraft; I _x - the moment of inertia of the spacecraft around the longitudinal axis; ω ₀ - absolute absolute velocity module of the orbital coordinate system.

The prototype method allows to increase the accuracy of the uniaxial orientation of the specifically considered type of spacecraft and, thereby, also reduce microloading on the spacecraft that occurs when the spacecraft is swinging and the transition to uncontrolled rotation mode. In the general case, the rotation of the spacecraft with the indicated speed is not stable for all types of spacecraft of an elongated shape - in the general case, with time, the deviation of the longitudinal axis of the spacecraft from the direction to the center of the earth becomes more and more significant, which leads to a "somersault" of the spacecraft and the destruction of the gravitational orientation. This also limits the possibility of conducting experiments requiring the guidance of scientific equipment to the Earth and / or a low level of microacceleration.

The problem to which the present invention is directed, is to increase the accuracy of the uniaxial orientation of the spacecraft when performing experiments and research in the conditions of the rotational motion of the spacecraft.

The technical result of the invention is to ensure the implementation of the gravitational orientation of the spacecraft with a spin at long time intervals with the evolution of the angular velocity of rotation of the spacecraft in the direction of acceleration.

при значении угла между радиус-вектором космического аппарата и вектором, направленным из центра масс космического аппарата в центр аэродинамического давления солнечных батарей космического аппарата, >90°,The technical result is achieved in that in a method of uniaxial orientation of a spacecraft of an elongated shape, including turns of a spacecraft and spin around its longitudinal axis corresponding to a minimum moment of inertia, the spacecraft is further deployed before spinning until the longitudinal axis of the spacecraft is aligned with the plane formed by the normal to the orbit plane and spacecraft radius vector, and reaching the angle between the plane of the orbit and the longitudinal axis of the spacecraft

when the angle between the radius vector of the spacecraft and the vector directed from the center of mass of the spacecraft to the center of aerodynamic pressure of the solar panels of the spacecraft,> 90 °,

where λ is the ratio of the minimum principal central moment of inertia to the average value of the transverse principal central moments of inertia of the spacecraft,

ω ₀ - the angular velocity of the orbital motion of the spacecraft,

ω ₁ - the absolute angular velocity of the spin of the spacecraft around its longitudinal axis,

, где α>1.after which spin the spacecraft around the longitudinal axis, and the magnitude of the angular velocity of the spin is determined by the ratio

, where α> 1.

Let us explain the proposed method of action.

We write the equations of the rotational motion of the spacecraft. The spacecraft is considered to be a solid body, the geocentric movement of its center of mass is Kepler elliptical. Elements of this movement are found according to the radio control of the orbit. To write the equations, we introduce two right Cartesian coordinate systems - the orbital OX ₁ X ₂ X ₃ and formed by the main central axes of inertia of the spacecraft Oh ₁ x ₂ x ₃ . Point O is the center of mass of the spacecraft, axes OX ₃ and OX _{1 are} directed, respectively, along the geocentric radius vector of the point O and are transversal to the orbit at this point. The axis O _{x1 is} directed along the longitudinal axis of the spacecraft.

, где a_i - косинус угла между осями ОХ_i и Ox_j.The position of the system Ox ₁ x ₂ x ₃ relative to the system OX ₁ X ₂ X ₃ will be given by the angles γ, δ and β, which we introduce as follows. The OX ₁ X ₂ X _{3 system} can be converted into the Ox ₁ x ₂ x _{3 system by} three successive turns: 1) by the angle δ + π / 2 around the OX axis ₂ , 2) by the angle β around the new OX axis ₃ , 3) by the angle γ about the new axis OX ₁ coinciding with the axis Ox ₁ . We denote the transition matrix from the Ox ₁ x ₂ x ₃ system to the OX ₁ X ₂ X _{3 system}

where a _i is the cosine of the angle between the axes OX _i and Ox _j .

Elements of this matrix are expressed through the introduced angles using formulas

In the equations of rotational motion of the spacecraft, gravitational and restoring aerodynamic moments are taken into account. These equations are written as

Here, ω _i (i = 1, 2, 3) are the components of the absolute angular velocity of the SC in the coordinate system Ox ₁ x ₂ x ₃ , ω ₀ is the angular velocity of the orbital motion of the SC, Ii are the moments of inertia of the SC relative to the axes Ox _i (main central moments inertia of the spacecraft), M _l is the restoring aerodynamic moment, calculated with respect to point O, applied to the spacecraft.

Equations (1) make it possible to estimate the rotational motion of the spacecraft under various conditions (Beletskii V.V. Motion of an artificial satellite relative to the center of mass. M., Nauka, 1965; Beletskii V.V. Motion of a satellite relative to the center of mass in a gravitational field. M .: Publishing House Moscow State University, 1975; F. Chernousko, On the Stability of the Regular Satellite Precession, Applied Mathematics and Mechanics, 1963, v. 28, issue 1, p. 155-157).

In the proposed method, the mode of gravitational orientation with a spin elongated along the longitudinal axis of the satellite is considered. In this mode, the satellite rotates around a longitudinal axis directed approximately along the local vertical. To apply this mode, three conditions must be met. First, the satellite must have a specific central ellipsoid of inertia: the major and middle semiaxes of this ellipsoid should not differ much from each other and be substantially larger (three or more times) of the minor semiaxis. Secondly, the gravitational moment applied to the satellite should significantly exceed other mechanical moments acting on the satellite. Thirdly, the satellite’s orbit should be close to circular. If the above conditions are fulfilled, then there may be satellite motions that are close to the so-called conical precession of an axisymmetric rigid body in a circular orbit with a small deviation of the axis of symmetry of the body from the local vertical.

In the case of an axisymmetric satellite in a circular orbit, its longitudinal axis in the nominal unperturbed mode lies in the plane passing through the radius vector of the center of mass and normal to the plane of the orbit, making an angle with the plane of the orbit

Here λ is the ratio of the minimum principal central moment of inertia (the moment of inertia of the spacecraft around the longitudinal axis I _x ) to the average value of the transverse principal central moments of inertia close in magnitude (average value of the moments of inertia of the spacecraft around the transverse axes of the spacecraft I _yz ), ω ₁ is the absolute angular velocity spacecraft spin around the longitudinal axis.

In the case λ << 1, even with a relatively large ratio | ω ₁ / ω ₀ | the angle β ₀ will be small. The longitudinal axis of the satellite with unequal moments of inertia, but satisfying the conditions listed above, will make small oscillations in the vicinity of the nominal position.

In this case, the nominal unperturbed motion of the satellite should be considered its motion, belonging to the two-dimensional integral variety of equations of motion. This manifold is constructed in the form of formal series for integer powers of small parameters characterizing perturbations. In particular, the perturbations caused by the difference between the satellite and the axisymmetric are characterized by the parameter μ = (I ₂ -I ₃ ) / I ₁ , where I ₂ ≈I ₃ ; disturbances caused by the ellipticity of the orbit are characterized by its eccentricity, etc. The indicated integral manifold is parameterized by two variables. One of them is close to the angular velocity ω ₁ , the second is close to the angle of rotation of the satellite around the longitudinal axis. For small parameters equal to zero, the integral manifold passes into the nominal mode of the axisymmetric satellite, and its parameters exactly coincide with ω ₁ and the indicated angle.

Formal series representing an integral manifold can not be constructed for all values of ω ₁ . For the construction to be possible, the values of ω ₀ and ω ₁ must be non-resonant. This refers to the absence of resonances between the oscillations of the longitudinal axis of the satellite in the vicinity of the above nominal position and the rotation of the satellite around this axis. Near resonance, the amplitude of oscillations of the longitudinal axis of the satellite in the vicinity of the nominal position increases rapidly, and the regime is destroyed.

It can be shown (V. Sarychev. Orientations of artificial satellites. - Results of the science of technology. Series of Space Research. T. 11. M.: VINITI, 1978; Hale J. Oscillations in nonlinear systems. M: Mir, 1966; Chernousko FL On the stability of a regular satellite precession, Applied Mathematics and Mechanics, 1963, v. 27, No. 3, p. 474; Bogolyubov NN, Mitropolsky Yu.A. Asymptotic Methods and Theory of Nonlinear Oscillations. M: Fizmatgiz , 1963; NN Moiseev, Asymptotic Methods of Nonlinear Mechanics, Moscow: Nauka, 1969; Heinbokel J., Strabl R.A. Periodic Decisions ia systems of differential equations with symmetry. - Mechanics. 1966. No. 1, p. 3; Poincare A. New methods of celestial mechanics. Selected works. Vol. 1 and 2. M .: Nauka, 1971-1972), that at λ << 1 "resonance" values of the angular velocity of rotation of the spacecraft defined by the equalities:

Here, the value of Ω is the rate of change of the angle of rotation of the spacecraft around the longitudinal axis, measured from the plane of the orbit.

In view of (3), the condition for the absence of resonances is expressed by the inequalities

or

The condition for the absence of resonances is quite insidious. The aerodynamic moment acting on the satellite makes ω ₁ slowly change - evolve. For this reason, even the non-resonant value of ω ₁ at the initial instant of time can become resonant with time. Near resonance, the amplitude of oscillations of the longitudinal axis of the satellite in the vicinity of the nominal position increases rapidly, and the regime is destroyed.

. При |β₀|<<1 колебания продольной оси КА в плоскости орбиты и относительно этой плоскости с точностью до членов порядка O(β₀) независимы и соответствующие им частоты приближенно равны

и

. Тогда условия (4) принимают видConditions (4) mean that the average angular velocity of the spacecraft rotation around the longitudinal axis should not be in resonance with the natural frequencies of this axis along the angles δ and β - angles that specify the position of the longitudinal axis of the spacecraft in the orbital coordinate system (β is the angle between the longitudinal axis The spacecraft and the orbit plane, δ is the angle between the projection of the longitudinal axis of the spacecraft on the orbital plane and the direction to the Earth). As indicated above, such frequencies ν are determined by the equation

. When | β ₀ | << 1, the oscillations of the longitudinal axis of the spacecraft in the plane of the orbit and relative to this plane are independent up to terms of the order of O (β ₀ ) and the frequencies corresponding to them are approximately equal

and

. Then conditions (4) take the form

и (6) соотношения для соответствующих «резонансных» значений угловой скорости вращения спутника ω₁ записываются в видеIf one of the inequalities of the first group (6) is violated, there is a resonance between the rotation of the spacecraft around the longitudinal axis and vibrations of this axis in the orbit plane (δ-resonance), if one of the inequalities of the second group (6) is violated, there is a resonance between the rotation of the spacecraft around the longitudinal axis and vibrations of this axis in the direction perpendicular to the plane of the orbit (β-resonance). Taking into account

and (6) the relations for the corresponding "resonant" values of the angular velocity of rotation of the satellite ω _{1 are} written in the form

For example, for a spacecraft with characteristic λ≈0.15 (for example, Progress transport cargo ship (TGK)), the values ν _δ / ω ₀ , ν _β / ω ₀ are ≈1.6 and ≈1.88, respectively, and the first-order resonance ( n = 1) is realized for the values of ω _{δ, 1} / ω ₀ and ω _{β, 1} / ω ₀ , respectively, ≈0.83 and ≈0.98.

We believe that the spacecraft is equipped with solar panels (SB) and that the center of aerodynamic pressure of the spacecraft is located on the longitudinal axis of the spacecraft. We carry out the uniaxial gravitational orientation of the spacecraft, taking into account the relative position of the centers of mass of the spacecraft, the earth and the center of aerodynamic pressure of the spacecraft.

We consider the orientation of the spacecraft in which the center of mass of the spacecraft is located between the centers of mass of the spacecraft and the earth - in this orientation, the angle between the radius vector of the spacecraft and the vector directed from the center of mass of the spacecraft to the center of aerodynamic pressure of the spacecraft is> 90 °. Then in the process of the evolution mentioned above | ω ₁ | increases if | ω ₁ | exceeds resonance values (7), then the spacecraft slowly unwinds, remaining close to solution (2). Otherwise, it is drawn into one of the resonances, in which the mode of oriented motion is rapidly destroyed.

т.е. начальное значение угловой скорости вращения КА должно определяется соотношениемThus, in the case when the center of aerodynamic pressure of the SB of the spacecraft is located between the centers of mass of the spacecraft and the earth, the condition for the long-term maintenance of the considered gravitational orientation mode is the excess of the maximum angular spin velocity of the satellite (7)

those. the initial value of the angular velocity of rotation of the spacecraft should be determined by the ratio

where the specified coefficient α> 1 determines the required excess of the angular velocity of the spin of the spacecraft over its maximum "resonant" value. The value of this coefficient is determined, inter alia, by the accuracy of constructing the required orientation and pulse development for spinning the spacecraft implemented by the spacecraft control system, and the requirement for the duration of maintaining the gravitational orientation.

As an example, let us cite the results of an analysis of the possibility of realizing a long (hundreds of turns) maintenance of gravitational orientation in the case when the center of aerodynamic pressure of the spacecraft SB is located between the center of mass of the spacecraft and the earth, for a spacecraft with characteristics λ≈0.15, ω ₀ ≈0.065 ° / s at height orbits of the order of 400 km and a turn duration of about 1.5 hours. For example, if the deviation of the longitudinal axis of the spacecraft from the local vertical is not more than 15 ° in (8), we can take α≈2 ÷ 2.6, which corresponds to the initial value of the angular velocity of rotation of the spacecraft ω ₁ ≈0.13 ÷ 017 ° / s, at which the initial deviation the longitudinal axis of the spacecraft from the local vertical is β ₀ ≈5 ÷ 6 °, while numerical simulation shows that the duration of maintaining the gravitational orientation until the angle between the longitudinal axis of the spacecraft and the local vertical reaches and begins to exceed 15 ° (i.e. . before violation th requirement for the accuracy of maintaining gravity orientation) is at least hundreds of turns.

We describe the technical effect of the invention.

The proposed method ensures the maintenance of the required parameters of the spacecraft orientation in the process of uncontrolled rotational motion for long (hundreds of turns) time intervals, namely, it ensures the implementation of the gravitational orientation of the spacecraft with swirling over long time intervals with the evolution of the angular velocity of the spacecraft in the direction of its acceleration.

The indicated result is achieved by spinning the spacecraft with the proposed angular velocity and from the proposed initial orientation, while the proposed spacecraft orientation parameters ensure that the longitudinal axis of the spacecraft oscillates in the vicinity of the described nominal position for the longest possible time and the subsequent evolution of the angular velocity of the spacecraft rotation toward its acceleration.

The proposed spin of the spacecraft from the proposed initial orientation over a long time interval “averages” the effect of the angular velocities around the transverse axes - the angular velocities around the transverse axes deviate the longitudinal axis of the spacecraft from a position that makes some angle with the local vertical, and then, due to the rotation of the spacecraft around the longitudinal axis, reduce this deviation and return the longitudinal axis of the spacecraft to a position that makes up the specified angle with the local vertical. At the same time, the proposed spin of the spacecraft around the longitudinal axis does not lead to gyroscopic stability of this axis in inertial space, and the spacecraft continues to move in orbit, while maintaining the described uniaxial orientation close to gravitational. Moreover, when implementing the described long-term regime of gravitational orientation with swirling, the angular velocity of the spacecraft rotates in the direction of acceleration (the spacecraft is “untwisted”).

Currently, everything is technically ready for the implementation of the proposed method for such a spacecraft as the Progress TGK. For the implementation of turns, twists and calculations, the standard means of the Progress TGK control system can be used — a motion and navigation control system, including an autonomous navigation system, solar sensors, angular velocity sensors, orientation engines, an on-board computer, etc.

Claims (1)

A method of uniaxial orientation of an elongated spacecraft, including turns of the spacecraft and a spin around its longitudinal axis corresponding to the minimum moment of inertia, characterized in that before spinning the spacecraft is deployed until the longitudinal axis of the spacecraft is aligned with the plane formed by the normal to the orbit plane and the radius -vector of the spacecraft, and reaching the angle between the plane of the orbit and the longitudinal axis of the spacecraft

,
where λ is the ratio of the minimum principal central moment of inertia to the average value of the transverse principal central moments of inertia of the spacecraft,
ω ₀ - the angular velocity of the orbital motion of the spacecraft,
ω ₁ - the absolute angular velocity of the spin of the spacecraft around its longitudinal axis,
if the angle is> 90 ° between the radius vector of the spacecraft and the vector directed from the center of mass of the spacecraft to the center of aerodynamic pressure of the solar panels of the spacecraft,
after which spin the spacecraft around the longitudinal axis, and the magnitude of the angular velocity of the spin is determined by the ratio

where α> 1.