CN109974691B - Large-scale space debris mechanical impact active despinning impact pose calculation method - Google Patents

Large-scale space debris mechanical impact active despinning impact pose calculation method Download PDF

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CN109974691B
CN109974691B CN201910269581.1A CN201910269581A CN109974691B CN 109974691 B CN109974691 B CN 109974691B CN 201910269581 A CN201910269581 A CN 201910269581A CN 109974691 B CN109974691 B CN 109974691B
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space debris
angular momentum
space
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张慧博
张德轩
马睿
姚金铭
戴士杰
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Hebei University of Technology
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Abstract

The invention relates to a method for calculating an active racemization impact pose of mechanical impact of a large space fragment. Compared with the prior mode of random impact for racemization, the working efficiency is improved, the impact is ensured not to increase the angular momentum of space debris, and the safety of racemization operation is improved. In a simulation experiment, the method is used for racemization, and the total angular momentum of the space debris is reduced from 50668N-mm.s to 38211N-mm.s after one impact.

Description

Large-scale space debris mechanical impact active despinning impact pose calculation method
Technical Field
The invention relates to the technical field of space debris racemization, in particular to a method for calculating a large-scale space debris mechanical impact initiative racemization impact pose.
Background
The growth of large space fragments seriously threatens the safety and stability of the space environment, and the recovery treatment of the large space fragments is an important measure for ensuring the sustainable utilization of the space environment. Since space debris in the space loses the capability of adjusting the impact pose (the impact position and the impact force direction), and the space debris runs in an out-of-control state for a long time, complex rolling motion often occurs under the influence of the shooting moment such as sunlight pressure, gravity gradient and the like and the residual angular momentum of the space debris before failure. In such cases there is a significant risk of collision with the direct capture of the space debris, and so it is an important measure to optimise the space to despun it to a safe capture state. In the literature (Matunaga S, Kanzawa T, Ohkami Y. positional movement-damper for the capture of an uncontrolled flowing satellite [ J ]. Control engineering practice,2001,9(2): 199-.
Disclosure of Invention
The invention aims to solve the technical problem of providing a large space debris mechanical impact type active rotation-elimination impact pose calculation method, which can calculate the position of an impact point on a space debris, and can reduce the angular momentum of the space debris when the position is impacted by a machine so as to achieve the purpose of rotation elimination of the space debris.
In order to solve the technical problems, the invention adopts the technical scheme that: the method for calculating the active despun impact pose of mechanical impact of large space debris comprises the following steps:
firstly, calculating the angular momentum of the rotation shaft:
knowing the radius of the space debris as r, the length as l and the mass m of the space debris, wherein the center position of the shaft end of the space debris is a point A, and the mass center of the space debris is taken as an origin O;
knowing the position coordinate A (x, y, z) of the shaft end center position on the space debris at the time t and the angular velocity omega of the rotation shaft1Calculating a unit vector pointing from the origin O to the point A
Figure BDA0002017939850000011
According to
Figure BDA0002017939850000012
Calculating the moment of inertia J of the rotation axis1Finally according to
Figure BDA0002017939850000013
Figure BDA0002017939850000014
Calculating angular momentum of a rotating shaft
Figure BDA0002017939850000015
Secondly, calculating the angular momentum of the nutation axis and the precession axis:
knowing the speed V at the central position A of the shaft end on the space debris at the moment tA(VAx,VAy,VAz) Angular velocity omega of nutating shaft2Calculating the velocityUnit vector
Figure BDA0002017939850000016
Is provided with L2Unit vector of
Figure BDA0002017939850000017
Then
Figure BDA0002017939850000018
Calculating to obtain L2Unit vector of
Figure BDA0002017939850000019
According to
Figure BDA00020179398500000110
Calculating the moment of inertia J of the nutating and precessing axes of the space debris2Finally according to
Figure BDA00020179398500000111
Calculating angular momentum of nutating and precessing axes
Figure BDA00020179398500000112
Thirdly, calculating the total angular momentum of the space debris:
computing the total angular momentum of the space debris according to the vector composition principle of the vectors
Figure BDA00020179398500000113
Is composed of
Figure BDA00020179398500000114
At this time, the magnitude, direction and unit vector of the total angular momentum are calculated
Figure BDA00020179398500000115
Fourthly, calculating an impact position:
suppose that a certain impact position on the surface of the space debris is P1The center of the space debris is O, and the unknown number is s
Figure BDA0002017939850000021
Figure BDA0002017939850000022
Finding P1Coordinates of the points; according to
Figure BDA0002017939850000023
Calculating the sum of P1Another point of point symmetry about the center is P2Then the positions of two impact points of the space debris, namely P, are determined1、P2；
And fifthly, calculating an impact posture:
assuming positive pressure F on impactNThe coefficient of friction between the impact rubber ball and the surface of the space debris is defined as F ═ μ FNCalculating a friction force f; let the unit vector of the friction force be
Figure BDA0002017939850000024
This unit vector satisfies the following condition:
Figure BDA0002017939850000025
comparing the unit vector of the speed at the central position of the shaft end on the space debris at the time t in the second step
Figure BDA0002017939850000026
The satisfied condition is known
Figure BDA0002017939850000027
The impact force is the vector sum of the friction force and the positive pressure, i.e.
Figure BDA0002017939850000028
Compared with the prior art, the invention has the beneficial effects that:
compared with the conventional method for despinning in a random impact mode, the method for calculating the active despinning impact pose of the large space debris mechanical impact improves the working efficiency, ensures that the impact cannot increase the angular momentum of the space debris, and improves the safety of despinning operation. In a simulation experiment, the method is used for racemization, and the total angular momentum of the space debris is reduced from 50668N-mm.s to 38211N-mm.s after one impact.
Drawings
Fig. 1 is a schematic structural diagram of a space debris model.
Fig. 2 is a graph showing the change of the three-axis angular momentum after the application of force to the space debris in example 1.
Fig. 3 is a diagram of the total angular momentum change of the simulation experiment.
Detailed Description
The present invention is further explained with reference to the following examples and drawings, but the scope of the present invention is not limited thereto.
The invention discloses a method for calculating an active despinning impact pose of mechanical impact of large space debris, which comprises the following steps of:
firstly, calculating the angular momentum of the rotation shaft:
the space debris is equivalent to a cylindrical space debris model, the radius of the space debris is r, the length of the space debris is l, the central position of the upper shaft end of the space debris is a point A, the central position of the lower shaft end of the space debris is a point B, and the center of mass of the space debris is in a three-dimensional space coordinate system with an origin O;
knowing the position coordinate A (x, y, z) of the shaft end center position on the space debris at the time t and the angular velocity omega of the rotation shaft1The radius r of the space debris and the mass m of the space debris, and calculating a unit vector pointing to the point A from the origin O
Figure BDA0002017939850000029
According to
Figure BDA00020179398500000210
Calculating the moment of inertia J of the rotation axis1Finally according to
Figure BDA00020179398500000211
Calculating angular momentum of a rotating shaft
Figure BDA00020179398500000212
Secondly, calculating the angular momentum of the nutation axis and the precession axis:
knowing the speed V at the central position A of the shaft end on the space debris at the moment tA(VAx,VAy,VAz) Angular velocity omega of nutating shaft2Calculating the unit vector of the velocity
Figure BDA00020179398500000213
Suppose L2Unit vector of
Figure BDA00020179398500000214
This unit vector needs to satisfy three conditions:
Figure BDA00020179398500000215
Figure BDA00020179398500000216
to obtain L2Unit vector of
Figure BDA00020179398500000217
According to
Figure BDA00020179398500000218
Calculating the moment of inertia J of the nutating and precessing axes of the space debris2Finally according to
Figure BDA00020179398500000219
(
Figure BDA00020179398500000220
Correspond to
Figure BDA00020179398500000221
Correspond to
Figure BDA00020179398500000222
Correspond to
Figure BDA00020179398500000223
) Calculating angular momentum of nutating and precessing axes
Figure BDA00020179398500000224
Thirdly, calculating the total angular momentum of the space debris:
computing the total angular momentum of the space debris according to the vector composition principle of the vectors
Figure BDA0002017939850000031
Is composed of
Figure BDA0002017939850000032
At the moment, the size and the direction of the total angular momentum are calculated; the unit vector of the total angular momentum can then be obtained
Figure BDA0002017939850000033
Fourthly, calculating an impact position:
suppose that a certain impact position on the surface of the space debris is P1If the center of space debris is O and the unknown number is s, then
Figure BDA0002017939850000034
The following conditions need to be satisfied:
Figure BDA0002017939850000035
finding P1Coordinates of points, with P1Another point of point symmetry about the center is P2Need to satisfy
Figure BDA0002017939850000036
The positions of two impact points, i.e. P, of the space debris are determined1、P2(ii) a Satisfy the requirement of
Figure BDA0002017939850000037
Figure BDA0002017939850000038
This condition states P1、P2And the impact force can form couple moment about the origin point at the moment, so that the aim of reducing the angular momentum is fulfilled. Relative to sheetIn the aspect of point impact, the method of double-point impact in the text can ensure that space debris cannot translate, and improves the stability of impact operation.
And fifthly, calculating the impact posture (direction of force):
assuming positive pressure F on impactNThe coefficient of friction between the impact rubber ball and the surface of the space debris is defined as F ═ μ FNCalculating a friction force f; let the unit vector of the friction force be
Figure BDA0002017939850000039
This unit vector satisfies the following condition:
Figure BDA00020179398500000310
comparing the unit vector of the speed at the central position of the shaft end on the space debris at the time t in the second step
Figure BDA00020179398500000311
The satisfied condition is known
Figure BDA00020179398500000312
The impact force is the vector sum of the friction force and the positive pressure, i.e.
Figure BDA00020179398500000313
Examples
In the embodiment, the impact pose is calculated according to the method, the friction coefficient mu between the impact rubber ball and the surface of the space debris is 0.47, the physical parameters of the space debris are shown in table 1, and three values of the rotational inertia J in the table respectively represent the rotational inertia of the nutation axis, the precession axis and the rotation axis.
TABLE 1 physical parameters of racemic targets
Figure BDA00020179398500000314
The initial precession angular velocity of the space debris in the simulation was set to be about 3.69 deg./s and the nutation angle was set to be about 53.9 deg.. The impact force was set to 35N, 147s at the selected impact time, and the impact was performedThe time was set to 0.2 s. And substituting the motion parameters of the space debris model into the fourth step for calculation to obtain s which is 260mm, wherein the coordinate of the impact position is P1(740,-720,20)、P2(-740,720, -20). The results of the simulation study are shown in fig. 3. Fig. 2 shows the change of the three-axis angular momentum after the space debris is applied with force, and the three-axis angular momentum can be seen to be reduced to different degrees. It follows that using the shock strategy herein for racemization can reduce the three-axis angular momentum of the space debris simultaneously. As can be seen from FIG. 3, the total angular momentum of the space debris was reduced from 50668 Nmm.s to 38211 Nmm.s within 0.2s, and the racemization efficiency reached 24.59%.
Nothing in this specification is said to apply to the prior art.

Claims (1)

1. A large space debris mechanical impact active despinning impact pose calculation method comprises the following steps:
firstly, calculating the angular momentum of the rotation shaft:
the radius of a known space fragment is r, the length of the known space fragment is l, the mass of the known space fragment is m, the central position of the upper shaft end of the space fragment is an A point, and the mass center of the space fragment is taken as an origin O;
knowing the position coordinate A (x, y, z) of the shaft end center position on the space debris at the time t and the angular velocity omega of the rotation shaft1Calculating a unit vector pointing from the origin O to the point A
Figure FDA0002548483400000011
According to
Figure FDA0002548483400000012
Calculating the moment of inertia J of the rotation axis1Finally according to
Figure FDA0002548483400000013
Figure FDA0002548483400000014
Calculating angular momentum of a rotating shaft
Figure FDA0002548483400000015
Secondly, calculating the angular momentum of the nutation axis and the precession axis:
knowing the speed V at the central position A of the shaft end on the space debris at the moment tA(VAx，VAy，VAz) Angular velocity omega of nutating shaft2Calculating the unit vector of the velocity
Figure FDA0002548483400000016
Is provided with
Figure FDA0002548483400000017
Unit vector of
Figure FDA0002548483400000018
Then
Figure FDA0002548483400000019
Is calculated to obtain
Figure FDA00025484834000000110
Unit vector of
Figure FDA00025484834000000111
According to
Figure FDA00025484834000000112
Calculating the moment of inertia J of the nutating and precessing axes of the space debris2Finally according to
Figure FDA00025484834000000113
Figure FDA00025484834000000114
Calculating angular momentum of nutating and precessing axes
Figure FDA00025484834000000115
Thirdly, calculating the total angular momentum of the space debris:
computing the total angular momentum of the space debris according to the vector composition principle of the vectors
Figure FDA00025484834000000116
Is composed of
Figure FDA00025484834000000117
At this time, the magnitude, direction and unit vector of the total angular momentum are calculated
Figure FDA00025484834000000118
Fourthly, calculating an impact position:
suppose that a certain impact position on the surface of the space debris is P1The centroid of the space debris is the origin O, the unknown number is s, according to
Figure FDA00025484834000000119
Finding P1Coordinates of the points; according to
Figure FDA00025484834000000120
Calculating the sum of P1Another point of point symmetry about the center is P2Then the positions of two impact points of the space debris, namely P, are determined1、P2；
And fifthly, calculating an impact posture:
assuming positive pressure F on impactNThe coefficient of friction between the impact rubber ball and the surface of the space debris is defined as F ═ μ FNCalculating a friction force f; let the unit vector of the friction force be
Figure FDA00025484834000000121
This unit vector satisfies the following condition:
Figure FDA00025484834000000122
comparing the center of the shaft end on the space debris at the time t in the second stepUnit vector of velocity at location
Figure FDA00025484834000000123
The satisfied condition is known
Figure FDA00025484834000000124
The impact force is the vector sum of the friction force and the positive pressure, i.e.
Figure FDA00025484834000000125
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