CN102928891B - Equivalent mass point set method for utilizing part quality characteristic to calculate universal gravitation in satellite cavity - Google Patents

Abstract

The invention provides an equivalent mass point set method for utilizing a part quality characteristic to calculate universal gravitation in a satellite cavity, and the method comprises the following steps of: 1, designing and determining a part on a satellite according to task requirements; 2, utilizing a quality characteristic comprehensive measurement meter to measure the quality characteristic of a certain part determined by the step 1 and recording; 3, establishing a mathematical equation meeting an equivalent mass point set according to a measuring result of the step 2; 4, solving to obtain the needed equivalent mass point set according to the equation of the step 3; 5, calculating the universal gravitation and the gradient of the part according to the equivalent mass point set solved by the step 4; and 6, repeating the steps 2-5 and calculating the universal gravitation and the gradient of all the parts; and summating to obtain the universal gravitation and the gradient of the satellite in the cavity. According to the equivalent mass point set method, when the universal gravitation of a quality distribution complicated part on the satellite is calculated, the actually-detachable quality characteristic information can be utilized to realize the calculation of the universal gravitation by universal gravitation; and the shape of the parts does not cause influences and the equivalent mass point set method has a wider applicable range in engineering.

Description

Utilize gravitational equivalent Particle Group method in part quality property calculation satellite cavity

Technical field

The present invention relates to astrodynamics technical field, especially relate to one and utilize gravitational equivalent Particle Group method in part quality property calculation satellite cavity.

Background technology

Some take Fundamental Physics Experiments as the space tasks of task object, as detected gravitational waves and checking LISA and the ASTROD task of general relativity, the reference mass needing to be positioned at satellite cavity flies (see the article " integrated model (The LISAintegrated model) of LISA " of periodical " classical and quantum gravity " (Classical and Quantum Gravity) the 20th volume in 2003 and periodical " former nuclear physics B " (Nuclear Physics B) the 166th volume 153-158 page article " ASTROD (Laser synchrotron source) and ASTROD I " in 2007) along pure Attractive Orbit.Equally, utilize reference mass along the pure Attractive Orbit flight of near-earth, and obtain the pure Attractive Orbit of reference mass, can be used in accurately measuring earth gravity field (" adopting the pure Attractive Orbit of accurate formation flight technical limit spacing (Acquirement of pure gravity orbit using precision formation flying technology) " see periodical " international aerospace joint conference periodical " (Acta Astronautica) special issue article in 2012).For the scientific goal of these tasks, the satellite universal gravitation acted on inside cavity reference mass is a main perturbed force, affects the performance level (article " the remaining acceleration error of current LISA is estimated (Current errorestimates for LISA spurious accelerations) " see " classical and quantum gravity " (Classical and Quantum Gravity) the 21st volume the 5th phase S653-S660 page in 2004) of pure Attractive Orbit.The universal gravitation interference of the pure Attractive Orbit of accurate Calculation is the basis overcoming this interference thus improve pure Attractive Orbit performance.

In prior art, LISA model team establishes the numerical computation method of universal gravitation interference, the node quality adopting satellite finite element model to provide and position, and each unit is approximately particle and calculates its gravitation to reference mass, moment and gradient effect, then entire amount (article " LISA is from gravitation analytical model (Self-gravitymodeling for LISA) " see " classical and quantum gravity " (Classical and QuantumGravity) the 22nd volume the 10th phase S395-S402 page in 2005) is obtained to all unit summations.

But, this method utilizing dummy satellite to calculate universal gravitation interference, harsh to the mass distribution accuracy requirement of satellite finite element model, make the Accurate Model of the non-homogeneous parts of material very difficult.In pure gravitation aerial mission widely, method proposed by the invention can be adopted to utilize actual part quality characteristic accurate Calculation universal gravitation interference of surveying.

Summary of the invention

The object of the invention is to design and a kind ofly novel utilize gravitational equivalent Particle Group method in part quality property calculation satellite cavity, solve the problem.

To achieve these goals, the technical solution used in the present invention is as follows:

One utilizes gravitational equivalent Particle Group method in part quality property calculation satellite cavity, comprises step as follows:

Step 1, according to mission requirements, the parts on satellite are determined in design;

Step 2, utilizes mass property general measuring instrument, the mass property of a certain parts in the determined parts of measuring process 1 record;

Step 3, according to the measurement result of step 2, sets up the math equation that equivalent Particle Group meets;

Step 4, according to the equation of step 3, solves and obtains required equivalent Particle Group;

Step 5, according to the equivalent Particle Group that step 4 solves, calculates universal gravitation and the gradient thereof of these parts;

Step 6, repeats step 2-5, calculates universal gravitation and the gradient thereof of all parts, and summation obtains the universal gravitation of satellite in cavity and gradient thereof.

Preferably, the measurement result according to step 2 shown in described step 3, set up the math equation that equivalent Particle Group meets, specifically comprise:

If the quality recording a certain part B in step 2 is M _o, be o (X with reference to centroid position in rectangular coordinate system OXYZ _o, Y _o, Z _o), the moment of inertia matrix in this parts main shaft coordinate system oyxz is $\left(\begin{array}{ccc}{I}_{\mathrm{xx},o}& 0& 0\\ 0& I_{\mathrm{yy},o}& 0\\ 0& 0& I_{\mathrm{zz},o}\end{array}\right);$

If the equivalent Particle Group identical with described part B mass property comprises N _pGindividual particle, the quality of particle is designated as m _{pG, i}, i=1,2 ... N _pG, the coordinate in this parts main shaft coordinate system oyxz is followed successively by (x _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pG, then the math equation that equivalent Particle Group meets is:

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}=M_o$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(y_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{xx},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(x_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{yy},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{P,i}(x_{\mathrm{PG},i}^2+y_{\mathrm{PG},i}^2)=I_{\mathrm{zz},o}$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0.---\left(1\right)$

Preferably, shown in described step 5, according to the equivalent Particle Group that step 4 solves, calculate universal gravitation and the gradient thereof of these parts, specifically comprise:

Coordinate (the x of particle in equivalence Particle Group _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pGbe provide in the main shaft coordinate system of part B, the rotation matrix that the main shaft coordinate of part B is tied to reference to rectangular coordinate system is R _ob, then equivalent Particle Group with reference in rectangular coordinate system coordinate be

$(X_{\mathrm{PG},b,i},Y_{\mathrm{PG},b,i},Z_{\mathrm{PG},b,i})=(x_{\mathrm{PG},i},y_{\mathrm{PG},i},z_{\mathrm{PG},i})R_{\mathrm{ob}}^T+(X_o,Y_o,Z_o)---\left(2\right)$

Record equivalent Particle Group with reference to the above coordinate in rectangular coordinate system, then can utilize equivalent Particle Group calculating unit B a bit (X in cavity all the time ₀, Y ₀, Z ₀) universal gravitation:

$a_{\mathrm{PG},x}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{X_{\mathrm{PG},b,i}-X_0}{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2{]}^{3/2}}$

$a_{\mathrm{PG},y}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Y_{\mathrm{PG},b,i}-Y_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}---\left(3\right)$

$a_{\mathrm{PG},z}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Z_{\mathrm{PG},b,i}-Z_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}$

Equally, the universal gravitation gradient of equivalent Particle Group calculating unit B can be utilized.

$T=\left(\begin{array}{ccc}{V}_{\mathrm{xx}}& V_{\mathrm{xy}}& V_{\mathrm{xz}}\\ V_{\mathrm{yx}}& V_{\mathrm{yy}}& V_{\mathrm{yz}}\\ V_{\mathrm{zx}}& V_{\mathrm{zy}}& V_{\mathrm{zz}}\end{array}\right)---\left(4\right)$

$V_{\mathrm{xx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{2{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{zz}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2+2{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xy}}=V_{\mathrm{yx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Y_{\mathrm{PG},b,i}-Y_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xz}}=V_{\mathrm{zx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yz}}=V_{\mathrm{zy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(Y_{\mathrm{PG},b,i}-Y_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}.$

The so-called mass property general measuring instrument of the present invention, refers in satellite engineering, the equipment of the quality of instrumented satellite or certain parts, centroid position, moment of inertia,

When the object of the invention is the universal gravitation of complicated mass distribution parts on accurate Calculation satellite, utilize the mass property of parts to realize universal gravitation with second order accuracy and calculate.

The present invention utilizes gravitational equivalent Particle Group method in part quality property calculation satellite cavity to comprise: the mass property of satellite component Selection and Design, measurement component, solve the equivalent Particle Group identical with part quality characteristic, utilize the universal gravitation of equivalent Particle Group calculating unit, add and obtain the universal gravitation of satellite in cavity.

Described satellite component Selection and Design, is according to satellite task needs, determines the parts that will use.The mass property of described measurement component utilizes the integral test system measurement of measurement quality, barycenter and moment of inertia to obtain the quality of parts, barycenter and these quality characteristic values of moment of inertia.Described solves the equivalent Particle Group identical with part quality characteristic, is according to measuring the part quality characteristic value obtained, and sets up math equation that equivalent Particle Group must meet and solves the equivalent Particle Group obtaining needs.The universal gravitation of described utilization equivalence Particle Group calculating unit, being according to solving the equivalent Particle Group obtained, calculating universal gravitation and the gradient thereof of wherein each particle, adding and obtain universal gravitation and the gradient thereof of equivalent Particle Group i.e. parts.Described adds and obtains the universal gravitation of satellite in cavity, is to all parts related to, and by their universal gravitation and gradient summation thereof, obtains the universal gravitation of satellite in cavity and gradient thereof.

Beneficial effect of the present invention can be summarized as follows:

1, the present invention calculate satellite improve quality the universal gravitation of complex distribution parts time, the mass property information that reality can be surveyed can be utilized, realize gravitational calculating with second order accuracy, and not by the impact of component shape, engineering have the wider scope of application.

2, the inventive method is simple, implementation cost is cheap, and result of calculation is accurate.

Accompanying drawing explanation

Fig. 1. the main shaft coordinate system oyxz of reference rectangular coordinate system OXYZ and a certain part B, wherein o is the centroid position of part B in reference rectangular coordinate system, and x, y, z are to three principal axis of inertia being respectively part B.Rotation matrix from oyxz to OXYZ is R _ob.

Embodiment

In order to make technical matters solved by the invention, technical scheme and beneficial effect clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

One utilizes gravitational equivalent Particle Group method in part quality property calculation satellite cavity, comprises step as follows:

Step 1, according to mission requirements, the parts on satellite are determined in design;

Step 2, utilizes mass property general measuring instrument, the mass property of a certain parts in the determined parts of measuring process 1 record;

Step 3, according to the measurement result of step 2, sets up the math equation that equivalent Particle Group meets;

Step 4, according to the equation of step 3, solves and obtains required equivalent Particle Group;

Step 5, according to the equivalent Particle Group that step 4 solves, calculates universal gravitation and the gradient thereof of these parts;

Step 6, repeats step 2-5, calculates universal gravitation and the gradient thereof of all parts, and summation obtains the universal gravitation of satellite in cavity and gradient thereof.

Wherein, the measurement result according to step 2 shown in described step 3, set up the math equation that equivalent Particle Group meets, specifically comprise:

If the quality recording a certain part B in step 2 is M _o, be o (X with reference to centroid position in rectangular coordinate system OXYZ _o, Y _o, Z _o), the moment of inertia matrix in this parts main shaft coordinate system oyxz is $\left(\begin{array}{ccc}{I}_{\mathrm{xx},o}& 0& 0\\ 0& I_{\mathrm{yy},o}& 0\\ 0& 0& I_{\mathrm{zz},o}\end{array}\right);$

If the equivalent Particle Group identical with described part B mass property comprises N _pGindividual particle, the quality of particle is designated as m _{pG, i}, i=1,2 ... N _pG, the coordinate in this parts main shaft coordinate system oyxz is followed successively by (x _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pG, then the math equation that equivalent Particle Group meets is:

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}=M_o$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(y_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{xx},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(x_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{yy},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{P,i}(x_{\mathrm{PG},i}^2+y_{\mathrm{PG},i}^2)=I_{\mathrm{zz},o}$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0.---\left(1\right)$

Wherein, shown in described step 5, according to the equivalent Particle Group that step 4 solves, calculate universal gravitation and the gradient thereof of these parts, specifically comprise:

Coordinate (the x of particle in equivalence Particle Group _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pGbe provide in the main shaft coordinate system of part B, the rotation matrix that the main shaft coordinate of part B is tied to reference to rectangular coordinate system is R _ob, then equivalent Particle Group with reference in rectangular coordinate system coordinate be

$(X_{\mathrm{PG},b,i},Y_{\mathrm{PG},b,i},Z_{\mathrm{PG},b,i})=(x_{\mathrm{PG},i},y_{\mathrm{PG},i},z_{\mathrm{PG},i})R_{\mathrm{ob}}^T+(X_o,Y_o,Z_o)---\left(2\right)$

Record equivalent Particle Group with reference to the above coordinate in rectangular coordinate system, then can utilize equivalent Particle Group calculating unit B a bit (X in cavity all the time ₀, Y ₀, Z ₀) universal gravitation:

$a_{\mathrm{PG},x}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{X_{\mathrm{PG},b,i}-X_0}{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2{]}^{3/2}}$

$a_{\mathrm{PG},y}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Y_{\mathrm{PG},b,i}-Y_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}---\left(3\right)$

$a_{\mathrm{PG},z}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Z_{\mathrm{PG},b,i}-Z_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}$

Equally, the universal gravitation gradient of equivalent Particle Group calculating unit B can be utilized.

$T=\left(\begin{array}{ccc}{V}_{\mathrm{xx}}& V_{\mathrm{xy}}& V_{\mathrm{xz}}\\ V_{\mathrm{yx}}& V_{\mathrm{yy}}& V_{\mathrm{yz}}\\ V_{\mathrm{zx}}& V_{\mathrm{zy}}& V_{\mathrm{zz}}\end{array}\right)---\left(4\right)$

$V_{\mathrm{xx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{2{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2+{2(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{zz}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2+2{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xy}}=V_{\mathrm{yx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Y_{\mathrm{PG},b,i}-Y_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xz}}=V_{\mathrm{zx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yz}}=V_{\mathrm{zy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(Y_{\mathrm{PG},b,i}-Y_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}.$

Below illustrate the detailed process of calculating:

The mass property of parts comprises the moment of inertia matrix under quality, barycenter and a certain characteristic coordinates system.

Utilize integral test system, measurement obtains: the quality of a certain part B is M _o, be o (X with reference to centroid position in rectangular coordinate system OXYZ _o, Y _o, Z _o), the moment of inertia matrix in this parts main shaft coordinate system oyxz is $\left(\begin{array}{ccc}{I}_{\mathrm{xx},o}& 0& 0\\ 0& I_{\mathrm{yy},o}& 0\\ 0& 0& I_{\mathrm{zz},o}\end{array}\right);$

If the equivalent Particle Group identical with part B mass property comprises N _pGindividual particle, the quality of particle is designated as m _{pG, i}, i=1,2 ... N _pG, the coordinate in this parts main shaft coordinate system oyxz is followed successively by (x _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pG, then equivalent Particle Group meets following math equation

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}=M_o$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(y_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{xx},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}(x_{\mathrm{PG},i}^2+z_{\mathrm{PG},i}^2)=I_{\mathrm{yy},o},\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{P,i}(x_{\mathrm{PG},i}^2+y_{\mathrm{PG},i}^2)=I_{\mathrm{zz},o}$

$\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{x}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0,\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}{y}_{\mathrm{PG},i}{z}_{\mathrm{PG},i}=0---\left(1\right)$

Prove, meet equivalent Particle Group and the part B of above-mentioned equation, around any axle crossing barycenter, there is identical moment of inertia known.Then according to the second order expension of gravitation bit function, equivalent Particle Group and part B have identical universal gravitation result of calculation.Therefore, available equivalents Particle Group replaces part B to calculate the universal gravitation of its outside with second order accuracy, and it is very convenient in actual computation, only need the gravitation calculating each particle generation that equivalent Particle Group comprises, then sue for peace and just obtain the gravitation of equivalent Particle Group generation, the gravitation that namely replaced parts produce.

Solving equation group (1) just can obtain required equivalent Particle Group.Coordinate (the x of particle in equivalence Particle Group _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pGprovide in the main shaft coordinate system of part B.The rotation matrix that the main shaft coordinate of part B is tied to reference to rectangular coordinate system is R _ob, then equivalent Particle Group with reference in rectangular coordinate system coordinate be

$(X_{\mathrm{PG},b,i},Y_{\mathrm{PG},b,i},Z_{\mathrm{PG},b,i})=(x_{\mathrm{PG},i},y_{\mathrm{PG},i},z_{\mathrm{PG},i})R_{\mathrm{ob}}^T+(X_o,Y_o,Z_o)---\left(2\right)$

Record equivalent Particle Group with reference to the above coordinate in rectangular coordinate system, then can utilize equivalent Particle Group calculating unit B a bit (X in cavity all the time ₀, Y ₀, Z ₀) universal gravitation

$a_{\mathrm{PG},x}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{X_{\mathrm{PG},b,i}-X_0}{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2{]}^{3/2}}$

$a_{\mathrm{PG},y}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Y_{\mathrm{PG},b,i}-Y_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}---\left(3\right)$

$a_{\mathrm{PG},z}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{Z_{\mathrm{PG},b,i}-Z_0}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{3/2}}$

Equally, the universal gravitation gradient of equivalent Particle Group calculating unit B can be utilized.

$T=\left(\begin{array}{ccc}{V}_{\mathrm{xx}}& V_{\mathrm{xy}}& V_{\mathrm{xz}}\\ V_{\mathrm{yx}}& V_{\mathrm{yy}}& V_{\mathrm{yz}}\\ V_{\mathrm{zx}}& V_{\mathrm{zy}}& V_{\mathrm{zz}}\end{array}\right)---\left(4\right)$

$V_{\mathrm{xx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{2{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2+{2(Y_{\mathrm{PG},b,i}-Y_0)}^2-{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{zz}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-{(X_{\mathrm{PG},b,i}-X_0)}^2-{(Y_{\mathrm{PG},b,i}-Y_0)}^2+2{(Z_{\mathrm{PG},b,i}-Z_0)}^2}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xy}}=V_{\mathrm{yx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Y_{\mathrm{PG},b,i}-Y_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{xz}}=V_{\mathrm{zx}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(X_{\mathrm{PG},b,i}-X_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

$V_{\mathrm{yz}}=V_{\mathrm{zy}}=G\underset{i=1}{\overset{N_{\mathrm{PG}}}{\mathrm{\Σ}}}{m}_{\mathrm{PG},i}\frac{-3(Y_{\mathrm{PG},b,i}-Y_0)(Z_{\mathrm{PG},b,i}-Z_0)}{{[{(X_{\mathrm{PG},b,i}-X_0)}^2+{(Y_{\mathrm{PG},b,i}-Y_0)}^2+{(Z_{\mathrm{PG},b,i}-Z_0)}^2]}^{5/2}}$

After the universal gravitation obtaining each parts one by one and gradient thereof, all parts are sued for peace, just can obtain the universal gravitation of satellite in cavity and gradient thereof.

As fully visible, the present invention calculate satellite improve quality the universal gravitation of complex distribution parts time, the mass property information that reality can be surveyed can be utilized, realize gravitational calculating with second order accuracy, and not by the impact of component shape, engineering has the wider scope of application.

The present invention is described in detail in preferred embodiment above by concrete; but those skilled in the art should be understood that; the present invention is not limited to the above embodiment; within the spirit and principles in the present invention all; any amendment of doing, equivalent replacement etc., all should be included within protection scope of the present invention.

Claims (2)

1. utilize a gravitational equivalent Particle Group method in part quality property calculation satellite cavity, it is characterized in that, comprise step as follows:

Step 1, according to mission requirements, the parts on satellite are determined in design;

Step 2, utilizes mass property general measuring instrument, the mass property of a certain parts in the determined parts of measuring process 1 record;

Step 3, according to the measurement result of step 2, sets up the math equation that equivalent Particle Group meets;

Step 4, according to the equation of step 3, solves and obtains required equivalent Particle Group;

Step 5, according to the equivalent Particle Group that step 4 solves, calculates universal gravitation and the gradient thereof of these parts;

Step 6, repeats step 2-5, calculates universal gravitation and the gradient thereof of all parts, and summation obtains the universal gravitation of satellite in cavity and gradient thereof;

The measurement result according to step 2 shown in described step 3, set up the math equation that equivalent Particle Group meets, specifically comprise:

If the quality recording a certain part B in step 2 is M _o, be o (X with reference to centroid position in rectangular coordinate system OXYZ _o, Y _o, Z _o), the moment of inertia matrix in this parts main shaft coordinate system oyxz is

If the equivalent Particle Group identical with described part B mass property comprises N _pGindividual particle, the quality of particle is designated as m _{pG, i}, i=1,2 ... N _pG, the coordinate in this parts main shaft coordinate system oyxz is followed successively by (x _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pG, then the math equation that equivalent Particle Group meets is:

2. that states according to claim 1 utilizes gravitational equivalent Particle Group method in part quality property calculation satellite cavity, it is characterized in that: shown in described step 5, according to the equivalent Particle Group that step 4 solves, calculate universal gravitation and the gradient thereof of these parts, specifically comprise:

Coordinate (the x of particle in equivalence Particle Group _{pG, i}, y _{pG, i}, z _{pG, i}), i=1,2 ... N _pGbe provide in the main shaft coordinate system of part B, the rotation matrix that the main shaft coordinate of part B is tied to reference to rectangular coordinate system is R _ob, part B coordinate of any in cavity is (X ₀, Y ₀, Z ₀), then equivalent Particle Group with reference to the coordinate in rectangular coordinate system is being

Record equivalent Particle Group with reference to the above coordinate in rectangular coordinate system, then can utilize equivalent Particle Group calculating unit B a bit (X in cavity all the time ₀, Y ₀, Z ₀) universal gravitation:

Equally, the universal gravitation gradient of equivalent Particle Group calculating unit B can be utilized: