Calculation method of on-orbit inertia characteristics and flexible modal frequencies of two-axis solar array satellite

Abstract

The method for calculating the inertia characteristics and flexible modal frequency of a two-axis solar array satellite in orbit, considering the data interaction rules of the satellite mass characteristic information and flexible characteristic information as well as the variable configuration information of the satellite body, focusing on the key analysis parameters in the satellite flexible dynamics analysis and control system design, calculating the satellite center of mass, moment of inertia and non-constrained modal frequency according to the changes of the A and B axis rotation angles of the two-axis solar array driving mechanism of the satellite as well as the inertia and flexible characteristic parameters of the satellite. Meanwhile, combining the damping of the flexible accessories of the satellite, the changes of the non-constrained modal complex frequency are calculated, which is used to solve the problems of calculating and analyzing the inertia characteristic parameters and flexible characteristic parameters of the variable configuration satellite, and provides a design basis for the satellite flexible dynamics analysis and control system design.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of spacecraft on-orbit inertia characteristic and flexible frequency calculation analysis method, especially according to the mass inertia of satellite center body, flexible antenna and solar wing and flexible characteristic, and the position relationship of attachment installation calculates system centroid, inertia and the change condition of flexible attachment frequency. BACKGROUND

[0002] Large space flexible structure, such as large SAR satellite, communication satellite etc., presents the characteristics of lightweight, variable configuration in orbit.In the process of on-orbit operation, due to the rotation of solar sail, the centroid of the star, the moment of inertia, the non-constrained modal frequency changes, which brings uncertainty to the design of the attitude control system on the satellite. To solve the above problems, the change of the satellite mass characteristics and the change of the flexible modal frequency need to be calculated according to the change of the active attachment.

[0003] The Chinese patent with publication number CN106295196A and the name of an on-orbit modal calculation method for a satellite with a rotating flexible solar array, in view of the above problems, studies the calculation method of satellite moment of inertia and non-constrained modal frequency under the condition of single-wing solar sail rotating around single axis.

[0004] However, the existing large flexible satellite will adopt a double-axis solar sail driving mechanism to control the rotation of the satellite solar wing to increase the charging efficiency of the solar wing. Due to the rotation of the B-axis of the satellite solar sail driving mechanism, the satellite configuration changes greatly, and the parameters such as the centroid of the satellite, the moment of inertia and the flexible vibration frequency change greatly, the dynamics parameters change more significantly, which increases the uncertainty of the system design. The above patent technology cannot be used to calculate and analyze the on-orbit inertia characteristics and flexible frequency of the satellite with double-axis solar sail. SUMMARY

[0005] The technical problem solved by the present application is to overcome the shortcomings of the prior art, to comprehensively consider the data interaction rules of satellite mass characteristic information and flexible characteristic information and satellite variable configuration information, to focus on the key analysis parameters in satellite flexible dynamics analysis and control system design, and to provide a calculation and analysis method for on-orbit inertia characteristics and flexible frequency of a satellite with double-axis solar sail. According to the change of the A-axis and B-axis rotation angle of the satellite double-axis solar sail driving mechanism and the inertia and flexible characteristic parameters of the satellite, the centroid of the satellite, the moment of inertia and the non-constrained modal frequency are calculated. At the same time, combined with the damping of the satellite flexible attachment, the change of the non-constrained modal complex frequency is calculated, which is used to solve the problem of calculating and analyzing the inertia characteristic parameters and flexible characteristic parameters of the variable configuration satellite, and to provide design basis for the design of satellite flexible dynamics analysis and control system.

[0006] The technical solution of the present application is: a method for calculating the on-orbit inertia characteristics and flexible modal frequency of a two-axis solar panel satellite, comprising satellite center of mass calculation, satellite moment of inertia calculation, satellite accessory non-constrained modal frequency calculation, and satellite accessory non-constrained modal complex frequency calculation, wherein:

[0007] Position of satellite center of mass in the whole-satellite mechanical coordinate system The calculation method is as follows:

[0008]

[0009] Wherein: T is the matrix transpose, m C is the satellite central body mass, m SA is the south solar panel mass, m NA is the north solar panel mass, m AT is the flexible antenna mass, is the position of the satellite central body center of mass in the whole-satellite mechanical coordinate system, is the position of the origin of the south solar panel installation coordinate system in the whole-satellite mechanical coordinate system, is the position of the origin of the north solar panel installation coordinate system in the whole-satellite mechanical coordinate system, SSJ is the transfer matrix of the south solar panel installation coordinate system relative to the whole-satellite mechanical coordinate system, C NSJ is the transfer matrix of the north solar panel installation coordinate system relative to the whole-satellite mechanical coordinate system, is the position of the south solar panel center of mass in the south solar panel installation coordinate system, is the position of the north solar panel center of mass in the north solar panel installation coordinate system, C ATJ is the installation matrix of the flexible antenna installation coordinate system relative to the whole-satellite mechanical coordinate system, is the position of the flexible antenna center of mass in the flexible antenna installation coordinate system, is the position of the origin of the flexible antenna installation coordinate system in the whole-satellite mechanical coordinate system;

[0010] Moment of inertia of the satellite relative to its center of mass The calculation method is as follows:

[0011]

[0012] Wherein is the moment of inertia of the satellite central body relative to its center of mass, is the moment of inertia of the south solar panel relative to the satellite center of mass, is the moment of inertia of the north solar panel relative to the satellite center of mass, is the moment of inertia of the flexible antenna relative to the satellite center of mass;

[0013] Satellite appendage unconstrained modal frequency ω SATi The calculation method is as follows:

[0014]

[0015] Wherein, i=1, 2, …, n SAT , n SAT is the number of characteristic values of the matrix After eigenvalue decomposition, wherein the characteristic value greater than 0 is denoted as λ SATi , M SAT is the mass matrix of the flexible satellite system, K SAT is the stiffness matrix of the flexible satellite system.

[0016] Satellite appendage unconstrained modal complex frequency ω' SATi The calculation method is as follows:

[0017]

[0018] Wherein, i=1, 2, …, n SAT , the matrix A SAT is subjected to eigenvalue decomposition, and the characteristic values arranged in ascending order are -n SAT1 ±jω dSAT1 , -n SAT2 ±jω dSAT2 , …, The characteristic value not equal to 0 is denoted as -n SATi ±jω dSATi , and A SAT is the dynamic matrix of the flexible satellite system.

[0019] Further, the transfer matrix C SSJ of the south solar panel installation coordinate system relative to the whole satellite mechanical coordinate system is:

[0020]

[0021] Wherein, α SS , β SS are the A-axis and B-axis rotation angles of the south solar panel.

[0022] Further, the transfer matrix C NSJ of the north solar panel installation coordinate system relative to the whole satellite mechanical coordinate system is:

[0023]

[0024] Wherein, α NS , β NS are the A-axis and B-axis rotation angles of the north solar panel.

[0025] Further, the moment of inertia of the south solar array with respect to the satellite center of mass is is the moment of inertia of the south solar array with respect to its center of mass, (·) × is the skew-symmetric matrix composed of the components of the vector (·).

[0026] Further, the moment of inertia of the north solar array with respect to the satellite center of mass is is the moment of inertia of the north solar array with respect to its center of mass, (·) × is the skew-symmetric matrix composed of the components of the vector (·).

[0027] Further, the moment of inertia of the flexible antenna with respect to the satellite center of mass is is the moment of inertia of the flexible antenna with respect to its center of mass, (·) × is the skew-symmetric matrix composed of the components of the vector (·).

[0028] Further, the mass matrix M of the flexible satellite system SAT is:

[0029]

[0030] where n SS is the number of flexible modes of the south solar array, n NS is the number of flexible modes of the north solar array, n AT is the number of flexible modes of the flexible antenna, is the n SS x n SS identity matrix, is the n NS x n NS identity matrix, is the n AT x n AT identity matrix, is the n SS x n NS zero matrix, is the n SS x n AT zero matrix, is the n NS x n AT zero matrix,

[0031]

[0032]

[0033] and respectively are the translational and rotational coupling coefficients of the south solar array relative to the connection point in the south solar array mounting coordinate system, and respectively are the translational and rotational coupling coefficients of the north solar array relative to the connection point in the north solar array mounting coordinate system, and respectively are the translational and rotational coupling coefficients of the flexible antenna relative to the connection point in the flexible antenna mounting coordinate system.

[0034] Further, the stiffness matrix K of the flexible satellite system SAT is:

[0035]

[0036] where 0 3×3 is a zero matrix of order 3x3, is a zero matrix of order 3xn SS , is a zero matrix of order 3xn NS , is a zero matrix of order 3xn AT , Λ SS is an n SS xn SS frequency matrix of the south solar array, whose diagonal elements are 2πω SS1 , 2πω SS2 , …, and the rest elements are 0, Λ NS is an n NS xn NS frequency matrix of the north solar array, whose diagonal elements are 2πω NS1 , 2πω NS2 , …, and the rest elements are 0, Λ AT is an n AT xn AT frequency matrix of the north solar array, whose diagonal elements are 2πω AT1 , 2πω AT2 , …, and the rest elements are 0, the vibration frequencies of the south solar array are ω SS1 , ω SS2 , …, the vibration frequencies of the north solar array are ω NS1 , ω NS2 , …, The flexible antenna has the vibration frequency of ω AT1 , ω AT2 , …,

[0037] Further, the dynamic matrix A SAT of the flexible satellite system is:

[0038]

[0039]

[0040] Wherein, s SS is the damping matrix of the n SS × n SS order south solar sail, the diagonal elements are ξ SS1 , ξ SS2 , …, and the rest elements are 0, s NS is the damping matrix of the n NS × n NS order north solar sail, the diagonal elements are ξ NS1 , ξ NS2 , …, and the rest elements are 0, s AT is the damping matrix of the n AT × n AT order north solar sail, the diagonal elements are ξ AT1 , ξ AT2 , …, and the rest elements are 0, the damping of the south solar sail is ξ SS1 , ξ SS2 , …, the damping of the north solar sail is ξ NS1 , ξ NS2 , …, the damping of the flexible antenna is ξ AT1 , ξ AT2 , …,

[0041] The advantages of this invention compared to existing technologies are as follows: This invention calculates the changes in the satellite's center of mass and moment of inertia at different rotation angles based on the mass, center of mass position, moment of inertia, and origin position of the attachment installation coordinate system of the satellite's central body, flexible antenna, and solar panels. Furthermore, it calculates the unconstrained modal frequencies of the satellite at different rotation angles, as well as complex frequencies considering the damping characteristics of the attachments, based on the vibration frequency, damping coefficient, translational coupling coefficient, and rotational coupling coefficient of the flexible attachments. This invention is mainly used in the design of satellite attitude control systems to calculate the on-orbit inertia and flexibility characteristics of large flexible satellites. The input parameters are commonly used parameters in satellite design, and the related design methods are simple and easy to implement, possessing strong practicality. This method effectively solves the problem of calculating and analyzing the inertia and flexibility characteristic parameters of variable-configuration satellites. It can be directly used to calculate and analyze the on-orbit inertia and flexibility frequencies of satellites with dual-axis solar panels. It is an important part of the high-precision, high-stability control design of variable-configuration remote sensing satellites with large flexible attachments and can be extended to other large flexible remote sensing satellites that require calculation and analysis of center of mass, moment of inertia, and flexible vibration frequency. Attached Figure Description

[0042] Figure 1 A schematic diagram showing the composition and connection method of a dual-axis solar panel satellite;

[0043] Figure 2 This is a schematic diagram illustrating the computational principle of the method of the present invention;

[0044] Figure 3 This is a schematic diagram of the relative displacement of the satellite's center of mass in the whole satellite's mechanical coordinate system (relative to the zero position of the solar panel) in an embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram illustrating the relative change in the satellite's moment of inertia (relative to the zero-position state of the solar panel) in an embodiment of the present invention.

[0046] Figure 5 This is a schematic diagram of the unconstrained modal frequencies of the solar panel in an embodiment of the present invention;

[0047] Figure 6 This is a schematic diagram of the unconstrained modal complex frequencies of the solar panel in an embodiment of the present invention. Detailed Implementation

[0048] This invention relates to a satellite with dual-axis flexible solar panels and a flexible antenna. The satellite consists of a central satellite body (excluding the south solar panel, north solar panel, and flexible antenna, hereinafter the same), a north solar panel, a south solar panel, and a flexible antenna. The connection method between the dual-axis solar panel satellite components and their individual units is as follows: Figure 1 As shown.

[0049] Figure 1 The main coordinate system is defined as follows:

[0050] (1)Satellite mechanical coordinate system O J X J Y J Z J : Coordinate origin O J Located at the theoretical center of the docking ring on the satellite-rocket separation plane; O J Z J Axis passing through the coordinate origin O J , perpendicular to the satellite-rocket separation plane, along the longitudinal axis direction of the satellite, the positive direction points to the ground; O J X J Axis passing through the coordinate origin O J , located in the satellite-rocket separation plane, parallel to the theoretical normal direction of the satellite east panel, the positive direction is consistent with the outer normal direction of the east panel, pointing to the normal flight direction of the satellite; O J Y J Axis passing through the coordinate origin O J , located in the satellite-rocket separation plane, perpendicular to the O J X J axis and the O J Z J axis, forming a right-handed system.

[0051] (2)Satellite center body coordinate system O C X C Y C Z C : Coordinate origin O C Located at the center of mass of the satellite center body, the O C X C , O C Y C , O C Z C axis of the coordinate system coincides with the O J X J , O J Y J , O J Z J axis of the satellite mechanical coordinate system in turn.

[0052] (3)South solar panel installation coordinate system O S X S Y S Z S : Coordinate origin O S Located at the connection between the root of the south solar panel and the satellite center body, when the south solar panel is not rotated, the O S X S , O S Y S , O S Z S axis of the coordinate system coincides with the O J X J , OJ Y J 、O J Z J axes coincide. When the biaxial sailboard rotates, the O S X S Y S Z S of the south sailboard mounting coordinate system O J X J Y J Z J rotates according to the 21 rotation sequence, first rotates by an angle a S Y S about the O SS X S axis, and then rotates by an angle β S X SS about the O S Y S axis. The A axis of the south sailboard corresponds to the O S X S axis, and the B axis corresponds to the O

[0053] (4) The north sailboard mounting coordinate system O N X N Y N Z N , with the coordinate origin O N located at the joint between the root of the north sailboard and the satellite central body. When the north sailboard does not rotate, the O N X N , O N Y N , and O N Z N axes of the coordinate system coincide with the O J X J , O J Y J , and O J Z J axes of the satellite mechanical coordinate system. When the biaxial sailboard rotates, the O N X N Y N Z N of the north sailboard mounting coordinate system O J X J Y J Z J rotates according to the 21 rotation sequence, first rotates by an angle a N Y N about the O NS X N axis, and then rotates by an angle β N X NS about the O N YN The axis B corresponds to O N X N The axis.

[0054] (5) Flexible antenna installation coordinate system O AT X AT Y AT Z AT , the coordinate origin O AT Located at the joint of the flexible antenna root and the satellite central body, the O AT X AT , O AT Y AT , O AT Z AT Axis coincides with the O J X J , O J Y J , O J Z J Axis of the satellite mechanical coordinate system.

[0055] (6) Satellite body coordinate system O B X B Y B Z B , the coordinate origin O B Located at the satellite whole star (including satellite central body, south solar sail, north solar sail and flexible antenna, the same below) centroid, the O B X B , O B Y B , O B Z B Axis coincides with the O J X J , O J Y J , O J Z J Axis of the satellite mechanical coordinate system.

[0056] The satellite structure and its coordinate system definition relationship described above, can refer to the satellite on-orbit modal frequency calculation method of different angles of solar wing, spacecraft engineering, 2017-08; CN106295196A, a kind of on-orbit modal calculation method of satellite with rotating flexible solar array; and flexible satellite on-orbit non-constrained modal calculation research, journal of aerospace, 2014-04.

[0057] As Figure 2 The calculation principle diagram of the method of the application is shown, the quantities that need to be obtained in advance include:

[0058] The A axis and B axis angle α of the south solar sail SS , β SS, unit rad

[0059] North solar array A and B axis rotation angle α NS , unit rad NS , unit rad

[0060] Satellite central body mass m C , unit kg

[0061] South solar array mass m SA , unit kg

[0062] North solar array mass m NA , unit kg

[0063] Flexible antenna mass m AT , unit kg

[0064] Position of satellite central body mass center in satellite mechanical coordinate system unit m

[0065] Position of south solar array mounting coordinate system origin in satellite mechanical coordinate system unit m

[0066] Position of north solar array mounting coordinate system origin in satellite mechanical coordinate system unit m

[0067] Position of south solar array mass center in south solar array mounting coordinate system unit m

[0068] Position of north solar array mass center in north solar array mounting coordinate system unit m

[0069] Position of flexible antenna mounting coordinate system origin in satellite mechanical coordinate system unit m

[0070] Flexible antenna mounting coordinate system mounting matrix C relative to satellite mechanical coordinate system ATJ

[0071] Position of flexible antenna mass center in flexible antenna mounting coordinate system unit m

[0072] Satellite central body moment of inertia relative to its mass center unit kgm 2

[0073] South solar array moment of inertia relative to its mass center unit kgm 2

[0074] North solar array moment of inertia relative to its mass center kg m 2

[0075] Moment of inertia of the flexible antenna about its center of mass kg m 2

[0076] Translational coupling coefficients of the south solar array in the south solar array mount frame with respect to the connection point kg 1 / 2 and rotational coupling coefficients kg 1 / 2 m

[0077] Translational coupling coefficients of the north solar array in the north solar array mount frame with respect to the connection point kg 1 / 2 and rotational coupling coefficients kg 1 / 2 m

[0078] Translational coupling coefficients of the flexible antenna in the flexible antenna mount frame with respect to the connection point kg 1 / 2 and rotational coupling coefficients kg 1 / 2 m

[0079] Natural frequencies of the south solar array ω SS1 , ω SS2 , …, Hz

[0080] Natural frequencies of the north solar array ω NS1 , ω NS2 , …, Hz

[0081] Natural frequencies of the flexible antenna ω AT1 , ω AT2 , …, Hz

[0082] Dampings of the south solar array ξ SS1 , ξ SS2 , …,

[0083] Dampings of the north solar array ξ NS1 , ξ NS2 , …,

[0084] Dampings of the flexible antenna ξ AT1 , ξ AT2 , …,

[0085] I. Center of mass of the satellite

[0086] The satellite center of mass calculation here refers to the calculation of the position of the center of mass of the satellite whole satellite (including the satellite central body, the south solar panel, the north solar panel and the flexible antenna) in the whole satellite mechanical coordinate system Unit: m, the specific calculation process is as follows:

[0087] (1) Calculate the transfer matrix C of the south solar panel installation coordinate system relative to the whole satellite mechanical coordinate system SSJ The specific calculation formula is as follows:

[0088]

[0089] (2) Calculate the transfer matrix C of the north solar panel installation coordinate system relative to the whole satellite mechanical coordinate system NSJ The specific calculation formula is as follows:

[0090]

[0091] (3) Calculate the position of the satellite center of mass in the whole satellite mechanical coordinate system The specific calculation formula is as follows:

[0092]

[0093] (·) T is the matrix transpose.

[0094] II. Satellite moment of inertia calculation

[0095] On the basis of the first part, the moment of inertia of the satellite whole satellite relative to its center of mass can be calculated Unit: kgm 2 The specific calculation process is as follows:

[0096] (1) Calculate the moment of inertia of the south solar panel relative to the satellite center of mass Unit: kgm 2 The specific calculation formula is as follows:

[0097]

[0098] (·) × is a skew-symmetric matrix composed of the components of the vector (·).

[0099] (2) Calculate the moment of inertia of the north solar panel relative to the satellite center of mass Unit: kgm 2 The specific calculation formula is as follows:

[0100]

[0101] (3) Calculate the moment of inertia of the flexible antenna relative to the satellite center of mass Unit: kg / m 2 The specific calculation formula is as follows:

[0102]

[0103] (4) Calculate the moment of inertia of the satellite relative to its center of mass. The specific calculation formula is as follows:

[0104]

[0105] III. Calculation of Unconstrained Modal Frequencies of Satellite Annexes

[0106] Calculate the unconstrained mode frequencies ω of the accessories (including the south solar panel, north solar panel, and flexible antenna) in a flexible satellite system consisting of a central body, a south solar panel, a north solar panel, and a flexible antenna. SAT1 ω SAT2 … The unit is Hz, and the specific calculation process is as follows:

[0107] (1) Calculate the rotational coupling coefficient of the south solar panel relative to the center of mass in the body coordinate system. Unit: kg 1 / 2 m is calculated using the following formula:

[0108]

[0109] (2) Calculate the rotational coupling coefficient of the north solar panel relative to the center of mass in the body coordinate system. Unit: kg 1 / 2 m is calculated using the following formula:

[0110]

[0111] (3) Calculate the translational coupling coefficient of the flexible antenna relative to the center of mass in the body coordinate system. Unit: kg 1 / 2 and rotational coupling coefficient Unit: kg 1 / 2 m is calculated using the following formula:

[0112]

[0113] (4) Calculate the mass matrix M of the flexible satellite system SAT and stiffness matrix K SAT The specific calculation formula is as follows:

[0114]

[0115]

[0116] where n SS is the order of the flexible mode of the south solar sail, n NS is the order of the flexible mode of the north solar sail, n AT is the order of the flexible mode of the flexible antenna; is the n SS × n SS order identity matrix, is the n NS × n NS order identity matrix, is the n AT × n AT order identity matrix; 0 3×3 is the 3 × 3 zero matrix, is the 3 × n SS zero matrix, is the 3 × n NS zero matrix, is the 3 × n AT zero matrix, is the n SS × n NS order zero matrix, is the n SS × n AT order zero matrix, is the n NS × n AT order zero matrix; Λ SS is the n SS × n SS order frequency matrix of the south solar sail, whose diagonal elements are 2πω SS1 , 2πω SS2 , …, and other elements are 0; Λ NS is the n NS × n NS order frequency matrix of the north solar sail, whose diagonal elements are 2πω NS1 , 2πω NS2 , …, and other elements are 0; Λ AT is the n AT × n AT order frequency matrix of the north solar sail, whose diagonal elements are 2πω AT1 , 2πω AT2 , …, and other elements are 0.

[0117] (5) perform eigenvalue decomposition on matrix to obtain eigenvalues in ascending order as λ SAT1 , λ SAT2 , …, Select the eigenvalue λ greater than 0 SATi , the satellite non-constrained modal frequency is calculated according to the following formula:

[0118]

[0119] Wherein, i = 1, 2, …, n SAT , n SAT The number of eigenvalues of the flexible satellite system is equal to n SS +n NS +n AT +3.

[0120] Four, satellite accessories non-constrained modal frequency calculation

[0121] The non-constrained modal complex frequency ω S ′ AT1 , ω S ′ AT2 , …, Hz of the satellite system composed of the satellite center body, the south solar panel, the north solar panel and the flexible antenna (including the south solar panel, the north solar panel and the flexible antenna) is calculated, and the specific calculation process is as follows:

[0122] (1) Calculate the damping matrix C of the flexible satellite system SAT The specific calculation formula is as follows:

[0123]

[0124] Wherein, s SS is the n SS × n SS order damping matrix of the south solar panel, and the diagonal elements are ξ SS1 , ξ SS2 , …, The rest of the elements are 0; s NS is the n NS × n NS order damping matrix of the north solar panel, and the diagonal elements are ξ NS1 , ξ NS2 , …, The rest of the elements are 0; s AT is the n AT × n AT order damping matrix of the north solar panel, and the diagonal elements are ξ AT1 , ξ AT2 , …, The rest of the elements are 0.

[0125] (2) Calculate the dynamic matrix A of the system SAT The specific calculation formula is as follows:

[0126]

[0127] (3) Perform eigenvalue decomposition on matrix A SAT , get the eigenvalues in ascending order as -n SAT1 ±jω dSAT1 , -n SAT2 ±jω dSAT2 , …, Select the eigenvalue not equal to 0 -n SATi ±jω dSATi , calculate the satellite non-constrained modal complex frequency according to the following formula:

[0128]

[0129] Wherein, i is equal to 1, 2, …, n SAT .

[0130] Embodiment

[0131] In order to verify the effectiveness of the present application, the method of the present application is verified by mathematical simulation.

[0132] Figure 3 The satellite center of mass in the whole satellite mechanical coordinate system relative to the solar panel is in zero position when the A axis of the satellite south and north solar panel changes from 0° to 360°, and the B axis is 0°, 20° and 40° in turn. The change of the satellite center of mass is given. The result analysis shows that the center of mass displacement of the satellite whole satellite caused by the change of the panel B axis is about 2.721x10 -6 m (Δy FCJ ).

[0133] Figure 4 The change of the satellite moment of inertia relative to the solar panel is given when the A axis of the satellite south and north solar panel changes from 0° to 360°, and the B axis is 0°, 20° and 40° in turn. The satellite moment of inertia is in zero position. The result analysis shows that the inertia change of the satellite whole satellite caused by the change of the panel B axis is about 2000kgm 2 (ΔI ZZSAT ).

[0134] Figure 5 The change of the satellite solar panel non-constrained modal frequency is given when the A axis of the satellite south and north solar panel changes from 0° to 360°, and the B axis is 0°, 20° and 40° in turn. The result analysis shows that the change of the satellite solar panel non-constrained modal frequency caused by the change of the panel B axis is about 0.0105Hz (ω SAT4 ).

[0135] Figure 6The change of the non-constrained modal complex frequency of the satellite solar panel is given when the A axis of the satellite solar panel in the south and north changes from 0° to 360° and the B axis is 0°, 20° and 40° in turn. The result analysis shows that the change of the non-constrained modal complex frequency of the satellite solar panel caused by the change of the B axis is about 0.0118 Hz (ω SAT4 ).

[0136] The content not described in detail in the specification of the present application is the known technology of the person skilled in the art.

Claims

1. A method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite, characterized by: This includes the calculation of the satellite's center of mass, the calculation of the satellite's moment of inertia, the calculation of the unconstrained modal frequencies of the satellite's appendages, and the calculation of the complex frequencies of the unconstrained modal frequencies of the satellite's appendages, among which: Position of the satellite's center of mass in the whole satellite's mechanical coordinate system The calculation method is as follows: in:(·) T For matrix transpose, m C For the mass of the satellite's central body, m SA For the mass of the South Solar Panel, m NA For the mass of the North Solar Panel, m AT For the quality of flexible antennas, This refers to the position of the satellite's center of mass in the entire satellite's mechanical coordinate system. The position of the origin of the coordinate system for the South Solar Panel in the overall satellite mechanical coordinate system. The position of the origin of the coordinate system for the North Solar Panel in the overall satellite mechanical coordinate system, C. SSJ The transfer matrix C for the south solar panel mounting coordinate system relative to the overall satellite mechanical coordinate system. NSJ Transition matrix for the coordinate system of the North Solar Panel relative to the mechanical coordinate system of the entire satellite. Let this be the position of the center of mass of the South Solar Panel in the South Solar Panel installation coordinate system. Let C be the position of the center of mass of the North Solar Panel in the North Solar Panel installation coordinate system. ATJ The mounting matrix for the flexible antenna mounting coordinate system relative to the overall satellite mechanical coordinate system. Let this be the position of the flexible antenna's centroid in the flexible antenna mounting coordinate system. The position of the origin of the flexible antenna mounting coordinate system in the overall satellite mechanical coordinate system; Moment of inertia of a satellite relative to its center of mass The calculation method is as follows: in Let be the moment of inertia of the satellite's central body relative to its center of mass. Let be the moment of inertia of the south solar panel relative to the satellite's center of mass. Let be the moment of inertia of the northern solar panel relative to the satellite's center of mass. Let be the moment of inertia of the flexible antenna relative to the satellite's center of mass; Satellite accessory unconstrained modal frequencies ω SATi The calculation method is as follows: Where i = 1, 2, ..., n SAT n SAT For the matrix The number of eigenvalues ​​after eigenvalue decomposition, where eigenvalues ​​greater than 0 are denoted as λ. SATi M SAT For the mass matrix of a flexible satellite system, K SAT The stiffness matrix of the flexible satellite system; Unconstrained modal complex frequencies ω' of satellite appendages SATi The calculation method is as follows: Where i equals 1, 2, ..., n SAT For matrix A SAT Eigenvalue decomposition yields eigenvalues ​​arranged in ascending order as -n. SAT1 ±jω dSAT1 -n SAT2 ±jω dSAT2 … Select a non-zero eigenvalue and denote it as -n. SATi ±jω dSATi A SAT The dynamic matrix for a flexible satellite system.

2. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The transfer matrix C of the southern solar panel mounting coordinate system relative to the overall satellite mechanical coordinate system SSJ for: Where α SS β SS The rotation angles of the A-axis and B-axis of the South Solar Panel.

3. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The transfer matrix C of the North Solar Panel Installation Coordinate System relative to the Overall Satellite Mechanical Coordinate System NSJ for: Where α NS β NS The rotation angles of the north solar panel are the A-axis and B-axis.

4. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The moment of inertia of the southern solar panel relative to the satellite's center of mass. for Let be the moment of inertia of the south solar panel relative to its center of mass, (·). × Let be a skew-symmetric matrix composed of the components of the vector (·).

5. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The moment of inertia of the northern solar panel relative to the satellite's center of mass. for Let be the moment of inertia of the North Solar Panel relative to its center of mass, (·). × Let be a skew-symmetric matrix composed of the components of the vector (·).

6. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The moment of inertia of the flexible antenna relative to the satellite's center of mass for Let be the moment of inertia of the flexible antenna relative to its center of mass, (·). × Let be a skew-symmetric matrix composed of the components of the vector (·).

7. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The mass matrix M of the flexible satellite system SAT for: Where, n SS Let n be the order of the flexible modes of the south solar panel. NS Let n be the order of the flexible modes of the North Solar Panel. AT Let the order of the flexible mode of the flexible antenna be [the order of the flexible mode]. For n SS ×n SS An identity matrix of order 1. For n NS ×n NS An identity matrix of order 1. For n AT ×n AT An identity matrix of order 1. For n SS ×n NS A zero matrix of order 1. For n SS ×n AT A zero matrix of order 1. For n NS ×n AT A zero matrix of order 1. and These represent the translational and rotational coupling coefficients of the South Solar Panel relative to the connection point in the South Solar Panel installation coordinate system, respectively. and These represent the translational and rotational coupling coefficients of the North Solar Panel relative to the connection point in the North Solar Panel installation coordinate system. and These are the translational coupling coefficient and rotational coupling coefficient of the flexible antenna relative to the connection point in the flexible antenna mounting coordinate system, respectively. The position of the satellite's center of mass in the satellite's mechanical coordinate system is given. The satellite comprises a central body, a south solar panel, a north solar panel, and a flexible antenna. × Let be a skew-symmetric matrix composed of the components of the vector (·).

8. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The stiffness matrix K of the flexible satellite system SAT for: Among them 0 3×3 It is a 3×3 zero matrix. For 3×n SS A zero matrix of order 1. For 3×n NS A zero matrix of order 1. For 3×n AT A zero matrix of order Λ SS For n SS ×n SS The frequency matrix of the south solar panel of order X, its diagonal elements are as follows: The remaining elements are 0, Λ NS For n NS ×n NS The frequency matrix of the North Solar Panel of order 1, its diagonal elements are as follows: The remaining elements are 0, Λ AT For n AT ×n AT The frequency matrix of the North Solar Panel of order 1, its diagonal elements are as follows: All other elements are 0, and the vibration frequencies of the South Solar Panel are as follows: The vibration frequencies of the northern solar panel are as follows: The vibration frequencies of the flexible antenna are as follows: n SS Let n be the order of the flexible modes of the south solar panel. NS Let n be the order of the flexible modes of the North Solar Panel. AT This represents the order of the flexible mode of the flexible antenna.

9. The method for calculating the on-orbit inertial characteristics and flexible mode frequencies of a dual-axis solar panel satellite according to claim 1, characterized in that: The dynamic matrix A of the flexible satellite system SAT for: Among them, s SS For n SS ×n SS The damping matrix of the order-1 south solar panel has diagonal elements as follows: All other elements are 0, s NS For n NS ×n NS The damping matrix of the order North Solar panel, its diagonal elements are as follows: All other elements are 0, s AT For n AT ×n AT The damping matrix of the order North Solar panel, its diagonal elements are as follows: All other elements are 0, and the damping of each order of the South Solar Panel is... The damping of the North Solar Panel is as follows: The vibration damping of the flexible antenna at each order is as follows n SS Let n be the order of the flexible modes of the south solar panel. NS Let n be the order of the flexible modes of the North Solar Panel. AT Λ represents the order of the flexible mode of the flexible antenna; SS For n SS ×n SS The frequency matrix of the south solar panel of order Λ NS For n NS ×n NS The frequency matrix of the north solar panel of order Λ AT For n AT ×n AT The frequency matrix of the North Solar Panel of order 1.

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