A method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters

Abstract

The present invention discloses a method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters. The method calculates the velocity increment of the spacecraft impacted by debris through changes in the spacecraft orbit, and obtains the momentum change of the spacecraft when the debris impacts the spacecraft in combination with the spacecraft mass. The torque change caused by the collision is obtained based on the angular velocity change of the gyroscope, and the vector of the collision point in the fixed coordinate system of the spacecraft body is obtained in combination with the momentum change. The expected mass of the debris is directly obtained based on the statistical average velocity distribution and momentum change of the space debris relative to the spacecraft. The present invention can directly obtain the spacecraft momentum change and angular momentum change, the expected mass of the debris, and the maximum and minimum masses of the debris corresponding to sudden changes in the spacecraft attitude and orbit parameters, which helps to estimate the long-term impact and statistical laws of the debris collision on the spacecraft on the orbit, helps to trace the source of space emergencies and diagnose and design disaster plans in the long-term management of the spacecraft, and assists in the effective implementation of anti-collision reinforcement in the spacecraft design process.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace engineering technology, and in particular relates to a method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters. Background Art

[0002] During spaceflight, spacecraft are susceptible to impacts from space debris, which can cause component failure or the disintegration of spacecraft materials and components. The LDEF long-duration exposure device launched by the United States was recovered after 5.7 years of orbit around the Earth, revealing over 32,000 visible debris impact craters on its surface. Debris of varying sizes and relative velocities can have varying impacts on spacecraft. Current methods calculate the likely impact time, mass, and velocity based on the cataloging parameters of collision debris. However, collision debris typically has extremely high relative velocities, and current methods cannot directly determine the expected mass of smaller fragments, as they are not included in the debris cataloging database. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters, which solves the problem that existing means cannot directly obtain the expected mass of collision debris.

[0004] The technical solution adopted by the present invention is: a method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters, including calculating the velocity increment of the spacecraft hit by debris through changes in the spacecraft orbit, and obtaining the momentum change of the spacecraft when the debris collides with the spacecraft in combination with the mass of the spacecraft; obtaining the torque change caused by the collision based on the angular velocity change of the gyroscope, and then obtaining the vector of the collision point in the fixed coordinate system of the spacecraft body in combination with the momentum change; and directly obtaining the expected mass of the debris based on the statistical average velocity distribution and momentum change of the space debris relative to the spacecraft.

[0005] The present invention is also characterized in that:

[0006] The specific steps include:

[0007] Step 1: Calculate the attitude matrix and determine the spacecraft orbit, and then calculate the velocity increment of the spacecraft when it is hit by debris;

[0008] Step 2: Calculate the momentum change of the debris colliding with the spacecraft based on the velocity increment;

[0009] Step 3: Calculate the component of the collision point position of the collision fragment in the fixed coordinate system of the spacecraft body and the angular momentum change of the spacecraft based on the change in the gyro angular velocity of the spacecraft and the corresponding change in the torque;

[0010] Step 4: Estimate the expected mass, maximum mass, and minimum mass of the debris based on the average velocity of the space debris relative to the spacecraft.

[0011] The specific calculation of the posture matrix in step 1 is:

[0012]

[0013] The transformation matrix from the reference coordinate system to the body coordinate system is:

[0014]

[0015] In step 2, the momentum change of the debris impacting the spacecraft is calculated using formula (50):

[0016] p=mv=MΔV (50)

[0017] In formula (50), p is the momentum, m is the debris mass, v is the debris velocity, M is the spacecraft mass, and ΔV is the velocity increment.

[0018] In step 3, the change in angular momentum is calculated using formula (51):

[0019] L=r×p=IΔΩ (51)

[0020] In formula (51), L is the change in angular momentum, I is the moment of inertia of the gyroscope in the spacecraft's body coordinate system, and ΔΩ is the change in gyroscope rotation speed.

[0021] Step 4 is as follows: Based on the average speed v of the fragments, assume the minimum speed v min and maximum speed v max , estimate the expected mass m and maximum mass m of the debris max and minimum mass m min :

[0022]

[0023]

[0024]

[0025] The beneficial effects of the present invention are as follows: the method of calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters can directly obtain the spacecraft momentum change and angular momentum change, the expected mass of the debris, and the maximum and minimum mass of the debris corresponding to the sudden changes in the spacecraft attitude and orbit parameters, which helps to estimate the long-term impact and statistical laws of debris collisions on the spacecraft on the orbit, helps to trace the source of space emergencies and disasters and design plans during the long-term management of spacecraft, and assists in the effective implementation of anti-collision reinforcement considerations during the spacecraft design process. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of flexible multi-body spacecraft modeling. DETAILED DESCRIPTION

[0027] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] The present invention provides a method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters. The method includes calculating the velocity increment of the spacecraft impacted by debris based on the change in the spacecraft orbit, and obtaining the momentum change of the debris impacting the spacecraft based on the spacecraft mass. The method also obtains the torque change caused by the collision based on the change in the angular velocity of the gyroscope, and then obtains the vector of the collision point in the fixed coordinate system of the spacecraft body based on the momentum change. The method also directly obtains the expected mass of the debris based on the statistical average velocity distribution and momentum change of the space debris relative to the spacecraft. The specific steps include:

[0029] Step 1. Calculate the velocity, acceleration and variation of each component in the flexible multi-body model of the spacecraft, such as Figure 1 As shown in Figure 1, the structure of the flexible multi-body spacecraft is modeled as a central rigid body with two solar wings. The solar wings rotate on a single axis to ensure that the angle between their normals and the sun is the minimum. b X b Y b Z b is the spacecraft body coordinate system, and O ls X ls Y ls Z ls and O rs X rs Y rs Z rs The left and right solar wing body coordinate systems (local coordinate systems) are established. c X c Y c Z c , origin O c Located in the spacecraft body coordinate system, the three axes are aligned with the spacecraft body coordinate system. The origin of the inertial coordinate system coincides with the origin of the center body, which is the initial position of the center body coordinate system. The position vector is defined as:

[0030] ar c :Any mass unit on the central body is in the central body coordinate system O c X c Y c Z c The radius vector in

[0031] b.ω c :The central body is relative to the inertial orbit coordinate system O o X o Y o Z o Angular velocity of rotation;

[0032] c. The i-th windsurfing board installation position is relative to the central body coordinate system O c X c Y c Z c Position radius vector;

[0033] d. When the i-th sailboard is not deformed, any mass unit is about the i-th sailboard coordinate system O pi X pi Y pi Z pi (O ls X ls Y ls Z ls and O rs X rs Y rs Z rs )’s position radius vector;

[0034] e. The elastic deformation vector of any mass unit of the i-th sailboard;

[0035] f.ω pi : The angular velocity of the sailboard relative to the central body (if the sailboard rotates, it can only rotate around the Y axis of the sailboard coordinate system, with one degree of freedom);

[0036] The radius vector of any mass unit on the central body with respect to the inertial coordinate system is

[0037] R=r c (1)

[0038] The velocity and acceleration of the mass unit relative to the inertial coordinate system are

[0039]

[0040]

[0041] The corresponding velocity variation is:

[0042]

[0043] The modal discretization of the sailboard is performed, and the elastic deformation of any point on the sailboard can be expressed using the modal expansion method as follows:

[0044]

[0045] Among them, M p is the mode number of the intercepted elastic vibration, is the modal vector of the i-th mode at the point, q piis the ith order modal displacement. Writing Equation (5) into matrix form, we have:

[0046]

[0047] where q p ={q p1 q p2 … q pMp} T is the modal displacement array, which we will use to represent the elastic vibration of the sailboard. is the modal matrix.

[0048] Obviously, the velocity and acceleration of this mass unit can be expressed as:

[0049]

[0050]

[0051] The radius vector of any mass unit on the sailboard with respect to the inertial coordinate system is:

[0052] R=r cp +r p +u p (9)

[0053] The velocity and acceleration corresponding to the mass unit relative to the inertial coordinate system are:

[0054]

[0055]

[0056] in, is the elastic deformation vector u of the mass unit p The time derivative in the sailboard coordinate system is, for The time derivative in the sailboard coordinate system is expressed in equations (7) and (8).

[0057] The sailboard can rotate around its Y axis, so it has one degree of freedom. Let its generalized coordinate of rotation be β p , then we can know

[0058]

[0059] The rotation law of the sailboard is known, so the velocity variation of any mass unit on the sailboard is:

[0060]

[0061] Step 2. Calculate the virtual power of each spacecraft component.

[0062] 1) Central body virtual power

[0063] The virtual power of the central body includes the virtual power of inertia force and the main power virtual power

[0064] a. Virtual power of inertia force

[0065]

[0066] Substituting equations (3) and (4) into equation (14), we have:

[0067]

[0068]

[0069] in,

[0070]

[0071]

[0072] E is the unit dyadic vector, J c,c is the moment of inertia of the central body relative to the origin of the central body coordinate system, and Q cr is the rotational coupled inertia force:

[0073] Q cr =ω c ×(J c,c ·ω c ) (19)

[0074] b. Active power virtual power

[0075] When the active force F (including control and interference forces) and torque T (including control and interference torque) of the spacecraft center body act on the origin of the center body coordinate system, the virtual power of the active force and active torque can be expressed as:

[0076]

[0077] 2) Windsurfing board virtual power

[0078] The sailboard is an elastic body, and its virtual power includes the inertial force virtual power Virtual strain energy change rate and the damping force virtual power

[0079] a. Virtual power of inertia force

[0080] Inertial force virtual power The expressions are:

[0081]

[0082] Substituting equations (10) and (11) into equation (21), the inertial force virtual power of the sailboard is:

[0083]

[0084] where δω c Related parts It can be expressed as:

[0085]

[0086] definition:

[0087] The moment of inertia J of the sailboard relative to the origin of the sailboard coordinate system after considering elastic deformation p :

[0088]

[0089] The moment of inertia J of the sailboard relative to the origin of the central body coordinate system after considering elastic deformation p,c :

[0090]

[0091] Coupling coefficient matrix of sailboard elastic vibration to spacecraft rotation

[0092]

[0093] Then formula (23) can be rewritten as:

[0094]

[0095] The coupled inertial force Q pr The expression is:

[0096]

[0097] in is the change in static moment caused by the elastic deformation of the sailboard (relative to the connection point of the sailboard); is the static moment of the sailboard relative to the origin of the central body coordinate system after considering the elastic deformation of the sailboard; is the static moment of the sailboard relative to the origin of the sailboard coordinate system after the elastic deformation of the sailboard is considered; Its physical meaning is the coupling coefficient matrix of the elastic vibration of the sailboard to the translational motion of the spacecraft.

[0098] In formula (22), p Related parts It can be expressed as:

[0099]

[0100] definition:

[0101] Coupling coefficient matrix of sailboard elastic vibration to sailboard rotation

[0102]

[0103] In the formula is the generalized modal mass matrix of the sailboard, and the generalized coupled inertial force Q pf The expression is:

[0104]

[0105] In formula (22), p Related parts It can be expressed as:

[0106]

[0107] The above formula can be rewritten as:

[0108]

[0109] The coupled inertial force Q ps The expression is:

[0110]

[0111] b. Virtual strain energy change rate

[0112] definition is the generalized modal stiffness matrix of the sailboard, then the rate of change of the virtual strain energy of the sailboard can be expressed in modal coordinates as:

[0113]

[0114] c. Damping force virtual power

[0115] Defined as is the generalized modal damping matrix of the sailboard, then the damping force virtual power of the sailboard can be expressed in modal coordinates as:

[0116]

[0117] d. Active power virtual power

[0118] The external force on the sailboard is mainly the driving torque, which is T p , then the active force virtual power is:

[0119]

[0120] Step 3. Calculate the spacecraft's virtual power.

[0121] Virtual power of inertial force of spacecraft system ∑δP I 、Main force virtual power ∑δP a and virtual strain energy change rate ∑δP e and damping force virtual power ∑δP d The virtual power expression of the entire spacecraft system is as follows:

[0122] 1) Active power virtual power

[0123]

[0124] 2) Virtual strain energy change rate

[0125]

[0126] 3) Damping force virtual power

[0127]

[0128] 4) Inertial force virtual power

[0129]

[0130] Step 4. Calculate the dynamic state of the entire spacecraft.

[0131] Variation δω c 、 Independent of each other, from the above formulas and based on the virtual power principle expression ∑δP I +∑δP a -∑δP e -∑δP d =0, we can get the dynamic equation of the entire spacecraft system.

[0132] 1) Spacecraft attitude dynamics equations

[0133]

[0134] After merging, we can get:

[0135]

[0136] Where J is the moment of inertia of the spacecraft system relative to the origin of the central body coordinate system, and its expression is:

[0137]

[0138] T is the main torque of the spacecraft as a whole, Q r The external force term for rotation is:

[0139]

[0140] 2) Dynamic equations of windsurfing board rotation

[0141] The dynamic equation for the rotation of the i-th sailboard is:

[0142]

[0143] 3) Dynamic equations of sailboard vibration

[0144] The dynamic equation of the vibration of the i-th sailboard is:

[0145]

[0146] Step 5. Calculate the attitude matrix based on the attitude angles obtained from the attitude dynamics equation. The Cardan angles of the 1-2-3 rotation are denoted as α, β, and γ respectively. The transformation matrices of the three transformations are:

[0147]

[0148] The transformation matrix from the reference coordinate system to the body coordinate system is:

[0149]

[0150] Step 6. Calculate the momentum of the debris relative to the spacecraft based on the velocity increment ΔV obtained from the spacecraft orbit determination.

[0151] p=mv=MΔV (50)

[0152] where p is the momentum, m is the mass of the debris, v is the velocity of the debris, and M is the mass of the spacecraft.

[0153] Step 7. Calculate the component of the collision point position r of the collision fragment in the fixed coordinate system of the spacecraft body and the angular momentum change of the spacecraft based on the change of the spacecraft attitude

[0154] L=r×p=IΔΩ (51)

[0155] Where L is the change in angular momentum, I is the moment of inertia of the gyroscope in the spacecraft's body coordinate system, and ΔΩ is the change in gyroscope rotational speed.

[0156] Step 8. According to the average speed of the fragments Assumed minimum speed v min and maximum speed v max , estimate the expected mass of the debris Maximum mass m max and minimum mass m min .

[0157]

[0158]

[0159]

[0160] Example

[0161] In the embodiment, the initial parameters of the satellite are: mass 2000kg, components of the inertia matrix I xx =3500,I xy =400,I xz =50,I yy =17000,I yz =30,I zz = 14000, the speed increment suddenly changes to 0.7mm / s. The speed increments of the three axes corresponding to the posture changes are 0mm / s, -0.7mm / s, and 1.0mm / s, with an average speed of 6km / s, a minimum speed of 1km / s, and a maximum speed of 12km / s.

[0162] Step 1. Calculate the velocity and acceleration of each component in the flexible multi-body model of the spacecraft, integrate to obtain the dynamic state of the spacecraft, calculate the attitude matrix of the spacecraft, and obtain the transformation matrix from the reference coordinate system to the body coordinate system.

[0163] Step 2. Calculate the momentum of the debris relative to the spacecraft as 2.2 kg·m / s based on the velocity increment of 0.7 mm / s obtained from the spacecraft orbit determination.

[0164] Step 3. Calculate the position of the collision point in the body's fixed coordinate system based on the posture change: [4.60.45-0.25]m.

[0165] Step 4. Calculate the expected mass of the fragments to be 0.36 kg, the maximum mass to be 2.2 kg, and the minimum mass to be 0.18 kg.

[0166] Through practical verification, it is found that the method of the present invention can quickly and directly calculate the spacecraft momentum change and angular momentum change corresponding to the sudden change of spacecraft attitude orbit parameters, the expected mass of the debris, and the maximum and minimum masses of the debris.

Claims

1. A method for calculating collision debris parameters through sudden changes in spacecraft attitude and orbit parameters, characterized in that: This includes calculating the velocity increment of the spacecraft when it is hit by debris through the change in the spacecraft's orbit, and obtaining the momentum change of the spacecraft when the debris hits the spacecraft based on the spacecraft's mass; obtaining the torque change caused by the collision based on the change in the angular velocity of the gyroscope, and then obtaining the vector of the collision point in the fixed coordinate system of the spacecraft body based on the momentum change; and directly obtaining the expected mass of the debris based on the statistical average velocity distribution and momentum change of the space debris relative to the spacecraft. The specific steps include: Step 1: Calculate the attitude matrix and determine the spacecraft orbit, and then calculate the velocity increment of the spacecraft affected by the debris collision; when calculating the attitude matrix, the Cardan angles of the 1-2-3 rotation are recorded as , the transformation matrices of the three transformations are: （48） The transformation matrix from the reference coordinate system to the body coordinate system is: （49） Step 2: Calculate the momentum change of the debris impacting the spacecraft based on the velocity increment using formula (50): （50） In formula (50), is momentum, is the fragment mass, is the fragmentation speed, is the spacecraft mass, is the speed increment; Step 3: Calculate the collision point position of the collision fragments according to the change of the spacecraft gyro angular velocity and the corresponding torque change using formula (51): The components of the fixed coordinate system of the aerospace body and the angular momentum change of the spacecraft: （51） In formula (51), is the change in angular momentum, is the moment of inertia of the gyroscope in the spacecraft's body coordinate system, is the change in gyro speed; Step 4: Estimate the expected mass, maximum mass, and minimum mass of the debris based on the average velocity of the debris relative to the spacecraft. , assuming a minimum speed and maximum speed , estimate the expected mass of the debris , maximum mass and minimum mass : （52） （53） （54）。

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