CN102928891B

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

Info

Publication number: CN102928891B
Application number: CN201210504671.2A
Authority: CN
Inventors: 张育林; 王兆魁; 谷振丰; 范丽
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2012-11-30
Filing date: 2012-11-30
Publication date: 2015-05-06
Anticipated expiration: 2032-11-30
Also published as: CN102928891A

Abstract

An equivalent mass point group method for calculating the gravitational force in a satellite cavity by using the mass characteristics of components. 1. Design and determine the components on the satellite according to the mission requirements; 3. According to the measurement results in step 2, establish the mathematical equation that the equivalent mass point group satisfies; 4. According to the equation in step 3, solve the required equivalent mass point group; 5. According to step 4 Calculate the gravitational force and its gradient of the component for the solved equivalent mass point group; 6. Repeat 2-5 to calculate the gravitational force and its gradient of all components, and sum to obtain the gravitational force and its gradient of the satellite in the cavity. When the present invention calculates the gravitational force of the components with complex mass distribution on the satellite, it can use the actually measurable mass characteristic information to realize the calculation of the universal gravitational force with the second-order accuracy, and it is not affected by the shape of the components, so it has a wide application range in engineering .

Description

Equivalent particle group method for calculating gravitational force in satellite cavity using component mass properties

技术领域technical field

本发明涉及航天动力学技术领域，尤其是涉及一种利用部件质量特性计算卫星腔体内万有引力的等效质点组方法。The invention relates to the technical field of aerospace dynamics, in particular to an equivalent mass point group method for calculating the gravitational force in a satellite cavity by using the mass characteristics of components.

背景技术Background technique

一些以基础物理实验为任务目标的空间任务，如探测引力波和检验广义相对论的LISA和ASTROD任务，需要位于卫星腔体内的参考质量沿着纯引力轨道飞行(参见期刊《经典与量子引力》(Classical and Quantum Gravity)2003年第20卷的文章“LISA的集成模型(The LISAintegrated model)”和期刊《原了核物理B》(Nuclear Physics B)2007年第166卷153-158页文章“ASTROD(激光天文动力学)and ASTROD I”)。同样，利用参考质量沿着近地纯引力轨道飞行，并获取参考质量的纯引力轨道，能够用于精确测量地球重力场(参见期刊《国际宇航联会刊》(Acta Astronautica)2012年特刊文章“采用精密编队飞行技术获取纯引力轨道(Acquirement of pure gravity orbit using precision formation flying technology)”)。对于这些任务的科学目标而言，卫星作用在腔体内部参考质量上的万有引力是一个主要的干扰力，影响纯引力轨道的性能水平(参见《经典与量子引力》(Classical and Quantum Gravity)2004年第21卷第5期S653-S660页的文章“当前的LISA残余加速度误差估计(Current errorestimates for LISA spurious accelerations)”)。精确计算纯引力轨道的万有引力干扰，是克服该项干扰从而提高纯引力轨道性能的基础。Some space missions with fundamental physics experiments as mission goals, such as the LISA and ASTROD missions to detect gravitational waves and test general relativity, require a reference mass located in the satellite cavity to fly along a purely gravitational orbit (see the journal "Classical and Quantum Gravity" ( Classical and Quantum Gravity) 2003 Volume 20 article "LISA integrated model (The LISA integrated model)" and journal "Original Nuclear Physics B" (Nuclear Physics B) 2007 Volume 166 153-158 article "ASTROD ( Laser Astrodynamics) and ASTROD I"). Similarly, using a reference mass to fly along a near-Earth purely gravitational orbit, and obtaining a reference mass's purely gravitational orbit, can be used to accurately measure the Earth's gravitational field (see Acta Astronautica 2012 special issue article " Acquirement of pure gravity orbit using precision formation flying technology"). For the scientific objectives of these missions, the satellite's gravitational force acting on the reference mass inside the cavity is a major disturbing force, affecting the performance level of a purely gravitational orbit (see Classical and Quantum Gravity 2004 Article "Current error estimates for LISA spurious accelerations" in Volume 21, Issue 5, pages S653-S660. Accurately calculating the gravitational disturbance of a purely gravitational orbit is the basis for overcoming the disturbance and improving the performance of a purely gravitational orbit.

现有技术中，LISA模型团队建立了万有引力干扰的数值计算方法，采用卫星有限单元模型提供的结点质量和位置，并将每个单元近似为质点计算其对参考质量的引力、力矩和梯度作用，然后对所有单元求和得到整体量(参见《经典与量子引力》(Classical and QuantumGravity)2005年第22卷第10期S395-S402页的文章“LISA自引力分析模型(Self-gravitymodeling for LISA)”)。In the prior art, the LISA model team has established a numerical calculation method for gravitational interference, using the mass and position of the nodes provided by the satellite finite element model, and approximating each unit as a mass point to calculate its gravitational, moment and gradient effects on the reference mass , and then sum all the units to get the overall quantity (see the article "Self-gravitymodeling for LISA ").

但是，这种利用卫星模型计算万有引力干扰的方法，对卫星有限单元模型的质量分布精度要求苛刻，使得材质非均匀部件的精确建模非常困难。在更广泛的纯引力飞行任务中，可以采用本发明所提出的方法利用实际可测的部件质量特性精确计算万有引力干扰。However, this method of calculating gravitational interference by using satellite models has strict requirements on the mass distribution accuracy of satellite finite element models, making accurate modeling of parts with non-uniform materials very difficult. In more extensive pure gravity flight missions, the method proposed by the invention can be used to accurately calculate the universal gravitational disturbance by using the actually measurable mass characteristics of components.

发明内容Contents of the invention

本发明的目的在于设计一种新型的利用部件质量特性计算卫星腔体内万有引力的等效质点组方法，解决上述问题。The purpose of the present invention is to design a new method of equivalent mass point group to calculate the gravitational force in the satellite cavity by using the mass characteristics of components to solve the above problems.

为了实现上述目的，本发明采用的技术方案如下：In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

一种利用部件质量特性计算卫星腔体内万有引力的等效质点组方法，包括步骤如下：A method for calculating the equivalent mass point group of the gravitational force in the satellite cavity by using the mass characteristics of the components, comprising the following steps:

步骤1，根据任务需求，设计确定卫星上的部件；Step 1, according to the mission requirements, design and determine the components on the satellite;

步骤2，利用质量特性综合测量仪，测量步骤1所确定的部件中的某一部件的质量特性并记录；Step 2, using a quality characteristic comprehensive measuring instrument to measure and record the quality characteristic of a certain part of the parts determined in step 1;

步骤3，根据步骤2的测量结果，建立等效质点组满足的数学方程；Step 3, according to the measurement result of step 2, establish the mathematical equation that the equivalent particle group satisfies;

步骤4，根据步骤3的方程，求解得到所需要的等效质点组；Step 4, according to the equation of step 3, solve to obtain the required equivalent mass point group;

步骤5，根据步骤4所求解的等效质点组，计算该部件的万有引力及其梯度；Step 5, calculate the gravitational force and its gradient of the part according to the equivalent particle group solved in step 4;

步骤6，重复步骤2-5，计算出所有部件的万有引力及其梯度，求和得到卫星在腔体内的万有引力及其梯度。Step 6, repeat steps 2-5, calculate the gravitational force and its gradient of all components, and sum to obtain the universal gravitational force and its gradient of the satellite in the cavity.

优选的，所述步骤3中所示的根据步骤2的测量结果，建立等效质点组满足的数学方程，具体包括：Preferably, according to the measurement result of step 2 shown in said step 3, establish the mathematical equation that the equivalent mass point group satisfies, specifically include:

设步骤二中测得某一部件B的质量为M_o，在参考直角坐标系OXYZ中质心位置为o(X_o，Y_o，Z_o)，在该部件主轴坐标系oyxz中的转动惯量矩阵为 $(\begin{matrix} I_{xx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$ Assume that the mass of a component B measured in step 2 is M _o , the position of the center of mass in the reference rectangular coordinate system OXYZ is o(X _o , Y _o , Z _o ), and the moment of inertia matrix in the component axis coordinate system oyxz for $(\begin{matrix} I_{xx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$

设与所述部件B质量特性相同的等效质点组包含N_PG个质点，质点的质量记为m_PG，i，i＝1，2，…N_PG，在该部件主轴坐标系oyxz中的坐标依次为(x_PG，i，y_PG，i，z_PG，i)，i＝1，2，…N_PG，则等效质点组满足的数学方程为：Assuming that the equivalent mass point group with the same mass characteristics as the part B contains N _PG mass points, the mass of the mass point is recorded as m _{PG, i} , i=1, 2, ... N _PG , and the coordinates in the component axis coordinate system oyxz (x _{PG, i} , y _{PG, i} , z _{PG, i} ), i=1, 2, ... N _PG , then the mathematical equation satisfied by the equivalent particle group is:

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} = = {M m}_{o o}$

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {x x}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {y the y}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {z z}_{PG PG,, i i} = = 00$

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} (({y the y}_{PG PG,, i i}^{22} + + {z z}_{PG PG,, i i}^{22})) = = {I I}_{xx xx,, o o},, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} (({x x}_{PG PG,, i i}^{22} + + {z z}_{PG PG,, i i}^{22})) = = {I I}_{yy yy,, o o},, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{P P,, i i} (({x x}_{PG PG,, i i}^{22} + + {y the y}_{PG PG,, i i}^{22})) = = {I I}_{zz zz,, o o}$

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {x x}_{PG PG,, i i} {y the y}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {x x}_{PG PG,, i i} {z z}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {y the y}_{PG PG,, i i} {z z}_{PG PG,, i i} = = 00 . . - - - - - - ((11))$

优选的，所述步骤5中所示的，根据步骤4所求解的等效质点组，计算该部件的万有引力及其梯度，具体包括：Preferably, as shown in the step 5, according to the equivalent mass point group solved in the step 4, the universal gravitation and its gradient of the component are calculated, specifically including:

等效质点组中质点的坐标(x_PG，i，y_pG，i，z_PG，i)，i＝1，2，…N_PG是在部件B的主轴坐标系中给出的，部件B的主轴坐标系到参考直角坐标系的旋转矩阵为R_ob，则等效质点组在参考直角坐标系中的的坐标为The coordinates of the particles in the equivalent particle group (x _{PG, i} , y _{pG, i} , z _{PG, i} ), i=1, 2, ...N _PG are given in the principal axis coordinate system of part B, and the The rotation matrix from the principal axis coordinate system to the reference rectangular coordinate system is R _ob , then the coordinates of the equivalent particle group in the reference rectangular coordinate system are

$(({X x}_{PG PG,, b b,, i i},, {Y Y}_{PG PG,, b b,, i i},, {Z Z}_{PG PG,, b b,, i i})) = = (({x x}_{PG PG,, i i},, {y the y}_{PG PG,, i i},, {z z}_{PG PG,, i i})) {R R}_{ob ob}^{T T} + + (({X x}_{o o},, {Y Y}_{o o},, {Z Z}_{o o})) - - - - - - ((22))$

记录等效质点组在参考直角坐标系中的以上坐标，则可以始终利用等效质点组计算部件B在腔体内一点(X₀，Y₀，Z₀)的万有引力：Record the above coordinates of the equivalent mass point group in the reference Cartesian coordinate system, then you can always use the equivalent mass point group to calculate the universal gravitation of part B at a point (X ₀ , Y ₀ , Z ₀ ) in the cavity:

${a a}_{PG PG,, x x} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{{X x}_{PG PG,, b b,, i i} - - {X x}_{00}}{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22} {]]}^{33 / / 22}}$

${a a}_{PG PG,, y the y} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{{Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{33 / / 22}} - - - - - - ((33))$

${a a}_{PG PG,, z z} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{{Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{33 / / 22}}$

同样，可以利用等效质点组计算部件B的万有引力梯度。Similarly, the gravitational gradient of component B can be calculated using the equivalent mass point group.

$T T = = (\begin{matrix} {V V}_{xx xx} & {V V}_{xy xy} & {V V}_{xz xz} \\ {V V}_{yx yx} & {V V}_{yy yy} & {V V}_{yz yz} \\ {V V}_{zx zx} & {V V}_{zy zy} & {V V}_{zz zz} \end{matrix}) - - - - - - ((44))$

${V V}_{xx xx} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{22 {(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} - - {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} - - {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

${V V}_{yy yy} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - {(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} - - {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

${V V}_{zz zz} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - {(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} - - {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + 22 {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

${V V}_{xy xy} = = {V V}_{yx yx} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - 33 (({X x}_{PG PG,, b b,, i i} - - {X x}_{00})) (({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

${V V}_{xz xz} = = {V V}_{zx zx} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - 33 (({X x}_{PG PG,, b b,, i i} - - {X x}_{00})) (({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

${V V}_{yz yz} = = {V V}_{zy zy} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - 33 (({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00})) (({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}} . .$

本发明所谓的质量特性综合测量仪，是指在卫星工程中，测量卫星或某部件的质量、质心位置、转动惯量的设备，The so-called quality characteristic comprehensive measuring instrument of the present invention refers to the equipment for measuring the mass, center of mass position and moment of inertia of a satellite or a certain component in satellite engineering,

本发明的目的是在精确计算卫星上复杂质量分布部件的万有引力时，利用部件的质量特性以二阶精度实现万有引力计算。The purpose of the present invention is to realize the calculation of universal gravitation with second-order precision by using the mass characteristics of the components when accurately calculating the universal gravitation of complex mass distribution components on the satellite.

本发明利用部件质量特性计算卫星腔体内万有引力的等效质点组方法包括：卫星部件选型设计、测量部件的质量特性、求解与部件质量特性相同的等效质点组、利用等效质点组计算部件的万有引力、加和得到卫星在腔体内的万有引力。The method of the present invention to calculate the equivalent mass point group of universal gravitation in the satellite cavity by using the mass characteristics of the components includes: selecting and designing the satellite components, measuring the mass properties of the components, solving the equivalent mass point groups with the same mass characteristics as the components, and calculating the components by using the equivalent mass point groups The sum of the universal gravitational force of and the satellite's universal gravitational force in the cavity is obtained.

所述的卫星部件选型设计，是根据卫星任务需要，确定要使用的部件。所述的测量部件的质量特性，是利用能够测量质量、质心和转动惯量的综合测试设备测量得到部件的质量、质心和转动惯量这些质量特性值。所述的求解与部件质量特性相同的等效质点组，是根据已经测量得到的部件质量特性值，建立等效质点组必须满足的数学方程并求解得到需要的等效质点组。所述的利用等效质点组计算部件的万有引力，是根据求解得到的等效质点组，计算其中每个质点的万有引力及其梯度，加和得到等效质点组也就是部件的万有引力及其梯度。所述的加和得到卫星在腔体内的万有引力，是对所有涉及到的部件，将它们的万有引力及其梯度求和，得到卫星在腔体内的万有引力及其梯度。The satellite component selection design is to determine the components to be used according to the satellite mission requirements. Said measuring the quality characteristics of the component is to use the comprehensive testing equipment capable of measuring mass, center of mass and moment of inertia to measure the quality characteristic values of the mass, center of mass and moment of inertia of the component. The said solution of the equivalent particle group having the same mass characteristic as the component is to establish a mathematical equation that the equivalent particle group must satisfy based on the measured component quality characteristic value, and obtain the required equivalent particle group by solving. The described calculation of the gravitational force of the component by using the equivalent mass point group is to calculate the gravitational force and its gradient of each mass point according to the equivalent mass point group obtained from the solution, and add the equivalent mass point group to obtain the universal gravitational force and its gradient of the component. The summing to obtain the gravitational force of the satellite in the cavity is to sum the gravitational force and its gradient of all related components to obtain the gravitational force of the satellite in the cavity and its gradient.

本发明的有益效果可以总结如下：Beneficial effects of the present invention can be summarized as follows:

1，本发明在计算卫星上质量分布复杂部件的万有引力时，能够利用实际可测的质量特性信息，以二阶精度实现万有引力的计算，且不受部件形状的影响，在工程上有较广的适用范围。1. When the present invention calculates the gravitational force of the complex mass distribution components on the satellite, it can use the actually measurable mass characteristic information to realize the calculation of the universal gravitational force with second-order accuracy, and it is not affected by the shape of the component, so it has a wide range of applications in engineering scope of application.

2，本发明方法简单、实施成本低廉，计算结果精确。2. The method of the present invention is simple, the implementation cost is low, and the calculation result is accurate.

附图说明Description of drawings

图1.参考直角坐标系OXYZ和某一部件B的主轴坐标系oyxz，其中o为部件B在参考直角坐标系中的质心位置，x，y，z向分别为部件B的三个惯量主轴。从oyxz到OXYZ的旋转矩阵为R_ob。Figure 1. The reference rectangular coordinate system OXYZ and the main axis coordinate system oyxz of a certain component B, where o is the position of the center of mass of component B in the reference rectangular coordinate system, and the x, y, and z directions are the three inertia axes of component B respectively. The rotation matrix from oyxz to OXYZ is R _ob .

具体实施方式Detailed ways

为了使本发明所解决的技术问题、技术方案及有益效果更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

其中，所述步骤3中所示的根据步骤2的测量结果，建立等效质点组满足的数学方程，具体包括：Wherein, according to the measurement result of step 2 shown in said step 3, establish the mathematical equation that the equivalent particle group satisfies, specifically include:

设步骤二中测得某一部件B的质量为M_o，在参考直角坐标系OXYZ中质心位置为o(X_o，Y_o，Z_o)，在该部件主轴坐标系oyxz中的转动惯量矩阵为 $(\begin{matrix} I_{xx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$ Assume that the mass of a component B measured in step 2 is M _o , the position of the center of mass in the reference rectangular coordinate system OXYZ is o(X _o , Y _o , Z _o ), and the moment of inertia matrix in the component axis coordinate system oyxz for $(\begin{matrix} I_{xxx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} = = {M m}_{o o}$

其中，所述步骤5中所示的，根据步骤4所求解的等效质点组，计算该部件的万有引力及其梯度，具体包括：Wherein, as shown in the step 5, according to the equivalent mass point group solved in the step 4, the universal gravitation and its gradient of the component are calculated, specifically including:

等效质点组中质点的坐标(x_PG，i，y_PG，i，z_PG，i)，i＝1，2，…N_PG是在部件B的主轴坐标系中给出的，部件B的主轴坐标系到参考直角坐标系的旋转矩阵为R_ob，则等效质点组在参考直角坐标系中的的坐标为The coordinates of the mass points in the equivalent mass point group (x _{PG, i} , y _{PG, i} , z _{PG, i} ), i=1, 2, ...N _PG are given in the principal axis coordinate system of part B, and the The rotation matrix from the principal axis coordinate system to the reference rectangular coordinate system is R _ob , then the coordinates of the equivalent particle group in the reference rectangular coordinate system are

${V V}_{yy yy} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - {(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {22 (({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} - - {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

以下举例说明计算的具体过程：The following example illustrates the specific process of calculation:

部件的质量特性包括质量、质心和某一特性坐标系下的转动惯量矩阵。The mass properties of a component include mass, center of mass, and moment of inertia matrix in a property coordinate system.

利用综合测试设备，测量得到：某一部件B的质量为M_o，在参考直角坐标系OXYZ中质心位置为o(X_o，Y_o，Z_o)，在该部件主轴坐标系oyxz中的转动惯量矩阵为 $(\begin{matrix} I_{xx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$ Using comprehensive testing equipment, it is measured that the mass of a certain component B is M _o , the position of the center of mass in the reference rectangular coordinate system OXYZ is o(X _o , Y _o , Z _o ), and the rotation in the component axis coordinate system oyxz The inertia matrix is $(\begin{matrix} I_{xx, o} & 0 & 0 \\ 0 & I_{yy, o} & 0 \\ 0 & 0 & I_{zz, o} \end{matrix});$

设与部件B质量特性相同的等效质点组包含N_PG个质点，质点的质量记为m_PG，i，i＝1，2，…N_PG，在该部件主轴坐标系oyxz中的坐标依次为(x_PG，i，y_PG，i，z_PG，i)，i＝1，2，…N_PG，则等效质点组满足以下数学方程Assume that the equivalent mass point group with the same quality characteristics as component B contains N _PG mass points, and the mass of the mass point is recorded as m _{PG, i} , i=1, 2, ... N _PG , and the coordinates in the component axis coordinate system oyxz are in turn: (x _{PG, i} , y _{PG, i} , z _{PG, i} ), i=1, 2,...N _PG , then the equivalent particle group satisfies the following mathematical equation

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} = = {M m}_{o o}$

${Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {x x}_{PG PG,, i i} {y the y}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {x x}_{PG PG,, i i} {z z}_{PG PG,, i i} = = 00,, {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} {y the y}_{PG PG,, i i} {z z}_{PG PG,, i i} = = 00 - - - - - - ((11))$

证明可知，满足上述方程的等效质点组与部件B，绕任意过质心的轴具有相同的转动惯量。则根据引力位函数的二阶展开可知，等效质点组与部件B具有相同的万有引力计算结果。因此，可用等效质点组代替部件B以二阶精度计算其外部的万有引力，且在实际计算中非常方便，只需要计算等效质点组所包含的每个质点产生的引力，然后求和就得到等效质点组产生的引力，也就是所代替的部件产生的引力。It can be proved that the equivalent mass point group satisfying the above equation and component B have the same moment of inertia around any axis passing through the center of mass. Then according to the second-order expansion of the gravitational potential function, it can be seen that the equivalent mass point group and the component B have the same gravitational calculation result. Therefore, the equivalent particle group can be used instead of component B to calculate its external gravitational force with second-order precision, and it is very convenient in actual calculation. It is only necessary to calculate the gravitational force generated by each particle contained in the equivalent particle group, and then sum to get The gravitational force produced by the equivalent mass point group is also the gravitational force produced by the replaced parts.

求解方程组(1)就可以得到所需要的等效质点组。等效质点组中质点的坐标(x_PG，i，y_PG，i，z_PG，i)，i＝1，2，…N_PG是在部件B的主轴坐标系中给出的。部件B的主轴坐标系到参考直角坐标系的旋转矩阵为R_ob，则等效质点组在参考直角坐标系中的的坐标为Solving the equation group (1) can obtain the required equivalent mass point group. The coordinates (x _{PG, i} , y _{PG, i} , z _{PG, i} ) of the particles in the equivalent particle group, i=1, 2, . . . N _PG are given in the principal axis coordinate system of part B. The rotation matrix from the principal axis coordinate system of part B to the reference rectangular coordinate system is R _ob , then the coordinates of the equivalent particle group in the reference rectangular coordinate system are

记录等效质点组在参考直角坐标系中的以上坐标，则可以始终利用等效质点组计算部件B在腔体内一点(X₀，Y₀，Z₀)的万有引力Record the above coordinates of the equivalent mass point group in the reference Cartesian coordinate system, then you can always use the equivalent mass point group to calculate the universal gravitation of part B at a point (X ₀ , Y ₀ , Z ₀ ) in the cavity

${V V}_{yz yz} = = {V V}_{zy zy} = = G G {Σ Σ}_{i i = = 11}^{{N N}_{PG PG}} {m m}_{PG PG,, i i} \frac{- - 33 (({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00})) (({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}{{[[{(({X x}_{PG PG,, b b,, i i} - - {X x}_{00}))}^{22} + + {(({Y Y}_{PG PG,, b b,, i i} - - {Y Y}_{00}))}^{22} + + {(({Z Z}_{PG PG,, b b,, i i} - - {Z Z}_{00}))}^{22}]]}^{55 / / 22}}$

逐个得到各部件的万有引力及其梯度之后，对所有部件求和，就可以得到卫星在腔体内的万有引力及其梯度。After obtaining the gravitational force and its gradient of each component one by one, the sum of all the components can be used to obtain the gravitational force and its gradient of the satellite in the cavity.

综上可见，本发明在计算卫星上质量分布复杂部件的万有引力时，能够利用实际可测的质量特性信息，以二阶精度实现万有引力的计算，且不受部件形状的影响，在工程上有较广的适用范围。In summary, when the present invention calculates the gravitational force of components with complex mass distribution on the satellite, it can use the actually measurable mass characteristic information to realize the calculation of gravitational force with second-order accuracy, and is not affected by the shape of the components. Wide scope of application.

以上通过具体的和优选的实施例详细的描述了本发明，但本领域技术人员应该明白，本发明并不局限于以上所述实施例，凡在本发明的精神和原则之内，所作的任何修改、等同替换等，均应包含在本发明的保护范围之内。The present invention has been described in detail above through specific and preferred embodiments, but those skilled in the art should understand that the present invention is not limited to the above-described embodiments, and within the spirit and principles of the present invention, any Modifications, equivalent replacements, etc., should all be included within the protection scope of the present invention.

Claims

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: