CN113311853A - Sun light pressure moment determination method for sun-centered orbit spacecraft - Google Patents

Sun light pressure moment determination method for sun-centered orbit spacecraft Download PDF

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CN113311853A
CN113311853A CN202110505403.1A CN202110505403A CN113311853A CN 113311853 A CN113311853 A CN 113311853A CN 202110505403 A CN202110505403 A CN 202110505403A CN 113311853 A CN113311853 A CN 113311853A
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pressure moment
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CN113311853B (en
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杨绍龙
金磊
李迎杰
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Beihang University
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Abstract

The invention discloses a method for determining sunlight pressure moment of a sun-centered orbit spacecraft, which is characterized by comprising the following steps of: the method comprises the following steps: step 1: establishing a projection coordinate system and obtaining a component array of the spacecraft under the projection coordinate system, wherein a centroid orbit coordinate system is taken as the projection coordinate system; step 2: shelter from the judgement to the spacecraft, obtain effective irradiation unit, mainly include: judging whether the micro elements are illuminated or not, eliminating mutual shielding among the parts and obtaining the micro elements which are actually illuminated; and step 3: determining the sunlight pressure moment on the spacecraft; and 4, step 4: and establishing an analytical expression of the sunlight pressure moment applied to the spacecraft, and further quickly obtaining the magnitude of the sunlight pressure moment. The light pressure moment calculation method provided by the invention has universality and higher calculation precision; the accuracy of calculating the sunlight pressure moment by using the expression is not reduced basically, and the calculation time can be effectively reduced.

Description

Sun light pressure moment determination method for sun-centered orbit spacecraft
[ technical field ] A method for producing a semiconductor device
The invention provides a novel method for determining sunlight pressure moment based on a sunlight pressure model for a sun-centered orbit spacecraft, and belongs to the technical field of overall design of spacecrafts.
[ background of the invention ]
With the continuous improvement of the requirement of the space mission, the attitude precision of the spacecraft is required to be higher. For a high orbit spacecraft with a deep space exploration task, most of the high orbit spacecraft provides energy for a load on a satellite through a solar sailboard, and due to the existence of the solar sailboard, sunlight pressure moment can not be ignored generally, so that the improvement of the attitude precision of the spacecraft is seriously influenced, and therefore, the sunlight pressure moment on the spacecraft needs to be accurately obtained.
The key for determining the sunlight pressure moment is to judge the shielding condition of the spacecraft in real time, and a few scholars have studied the sunlight pressure moment at present. The Liu frusta and the like perform projection transformation on a geometric body consisting of the satellite body and the solar sailboard, judge mutual shielding of the satellite body and calculate the effective acting area of the sunlight pressure by adopting a convex polygon intersection algorithm, so that the sunlight pressure moment is calculated, but the calculation process is relatively complex. Guo Jian et al consider the space station as a set of N rectangular planes, then divide each rectangle into square infinitesimals, and judge occlusion by judging the distance between the projected infinitesimals and each rectangular plane, but because the projected infinitesimals are uncertain in shape, the accuracy needs to be examined. The problem of how to simply, efficiently and accurately determine the magnitude of the sunlight pressure moment borne by the spacecraft is still a big problem.
Therefore, the invention provides a set of illumination shielding judgment process with simple algorithm and high universality, and provides a method for determining the optical pressure moment. According to the method provided by the invention, the illumination back of the spacecraft can be eliminated according to a surface vector method, the illumination surface is further subjected to shielding judgment to obtain an effective illumination unit, and finally, the light pressure moment borne by the spacecraft is determined according to a light pressure moment mathematical model, so that an analytical expression of the light pressure moment is obtained.
[ summary of the invention ]
The invention provides a method for determining sunlight pressure moment aiming at a sun-centered orbit spacecraft based on a sunlight pressure model, so that the sunlight pressure moment borne by the spacecraft is obtained.
Aiming at the problems, the technical scheme of the invention is as follows:
a projection coordinate system is established according to the motion characteristics of the spacecraft, a component array of the spacecraft under the projection coordinate system is obtained, so that the illumination back of the spacecraft is eliminated according to a surface vector method, the illumination face is shielded and judged, an effective illumination unit is obtained, finally, the light pressure moment borne by the spacecraft is determined according to a light pressure moment mathematical model, and an analytical expression of the light pressure moment is obtained. The specific operation steps are as follows:
step 1: and establishing a projection coordinate system and obtaining a component array of the spacecraft under the projection coordinate system. The method specifically comprises the following steps:
step 1.1: defining a coordinate system
a. Centroid inertial frame fe(oexeyeze)
Origin o of the centroid inertial frameeFixedly connected to the sun center oexeThe axis being in the plane of the spacecraft orbit and directed towards a certain star, oezeAxis perpendicular to the plane of the track, oeyeIn the plane of the track, andexeshaft oezeThe axes form a rectangular coordinate system.
b. Orbital coordinate system of the sun's center fo(ooxoyozo)
Origin o of the orbital coordinate system of the sunoIs fixedly connected with the mass center o of the spacecraftozoThe axis pointing to the sun center, ooxoThe axis lying in the plane of the sun-centered track, perpendicular to oozoAxis and pointing in the direction of motion of the spacecraft, ooyoShaft and ooxoShaft oozoThe axes form a rectangular coordinate system. The coordinate system follows the orbital motion of the spacecraft with an angular velocity omegaoAround ooyoNegative axial rotation, omegaoNamely the orbital angular velocity of the spacecraft.
c. Body coordinate system fb(obxbybzb)
The body coordinate system is fixedly connected with the spacecraft and has an origin obLocated in the center of mass of the spacecraft, obxbThe axis pointing in the direction of motion of the spacecraft, obzbThe axis is directed perpendicular to the flight trajectory plane below the aircraft,obybshaft and obxbShaft obzbThe axes form a rectangular coordinate system.
d. Sailboard fixed connection coordinate system fak(oakxakyakzak)
Origin o of sailboard fixed connection coordinate systemakThe three-axis direction is consistent with the coordinate system of the central body and the sailboard can wind around the axisakyakThe shaft rotates.
Step 1.2: rotation matrix calculation between coordinate systems
Defining a coordinates system f of the orbit of the centre of the sunoTo the body coordinate system fbA rotation matrix of RboBody coordinate system fbOrbital coordinate system f to the center of the sunoA rotation matrix of RobDefine a body coordinate system fbCoordinate system f for fixing to sailboardakA rotation matrix of RakbSailboard fixed connection coordinate system fakTo the body coordinate system fbA rotation matrix of Rbak. The attitude of the spacecraft is described by adopting the relative orientation of the main system and the heliocentric orbital system, the rotation sequence adopts 3-1-2,
Figure BDA0003058176080000033
theta and psi respectively represent the rolling angle, the pitch angle and the yaw angle of the spacecraft, and define the wind angle o of the sailboardakyakThe angle of rotation of the shaft being betak. So that:
Figure BDA0003058176080000031
Figure BDA0003058176080000032
Rob＝R′bo,Rbak＝R′akb (3)
step 1.3: coordinate transformation of spacecraft infinitesimal
Selecting a component array of a sun direction vector (a vector of an origin point of a body coordinate system pointing to the sun center) in a projection coordinate system of a sun center orbit coordinate systemos is:
os＝[0 0 1]T (4)
converting coordinate data of mass infinitesimal of each component of the spacecraft into a projection coordinate system, and dividing the coordinate data into a central body and a sailboard, wherein the expressions are respectively as follows:
orbi＝Rob brbi (5)
orbj＝Rob(brbak+Rbak akrakj) (6)
wherein the content of the first and second substances,brbiandorbirespectively representing the origin o of the body coordinate systembThe component arrays of the vector to the central body mass element under the body coordinate system and the projection coordinate system,akrakjindicating origin o of sailboard fixed coordinate systemakThe vector to the quality infinitesimal of the sailboard is a component array under the fixedly connected coordinate system of the sailboard,orbjrepresenting origin o of body coordinate systembA component array of vectors to the sail panel mass infinitesimal under a projection coordinate system,brbakrepresenting origin o of body coordinate systembTo the origin o of the coordinate system of the attachment of the sailboardakThe component array of the vector of (1) in the body coordinate system.
Step 2: and (4) shielding judgment is carried out on the spacecraft to obtain an effective irradiation unit. The method comprises the following specific steps:
step 2.1: eliminating the back side to obtain the irradiated surface
Dividing the surface of the spacecraft into a plurality of triangular patches by using finite element analysis software, and solving the component array of the normal vector of the patches in the projection coordinate system according to the component array of the vertices of the triangular patches in the projection coordinate systemon0The expression is:
Figure BDA0003058176080000041
wherein A, B, C respectively represent the three vertices of a triangular patch,orA、orB、orCand the vector matrixes from the origin of the projection coordinate system to the three vertexes of the triangular patch under the projection coordinate system are respectively expressed, and the | | r | | represents two norms of r.
Component array of patch external normal vector (normal vector pointing to outer side of spacecraft) in projection coordinate systemon is corrected through points on a triangular patch, and the expression is as follows:
on＝sign(orP·on0)on0 (8)
wherein the content of the first and second substances,orPand the vector from the origin of the projection coordinate system to the P point on the triangular surface plate is represented as a component array under the projection coordinate system, and sign (#) is a symbolic function.
By a function H (os·on) determining the surface to be irradiated:
Figure BDA0003058176080000051
wherein the content of the first and second substances,onzto representoZ-axis component of n, H: (os·on) — 1 denotes that the patch is irradiated, H: (os·on) — 0 indicates that the patch is occluded.
Step 2.2: occlusion determination between spacecraft components
Projecting all illuminated patches onto a projection surface, wherein the projection surface equation is as follows:
z＝h (10)
the projection pattern of the illumination surface is subjected to infinitesimal division, and if the infinitesimal is positioned in the projection of the surface patch, a positive number lambda exists1,λ2,λ3Such that:
Figure BDA0003058176080000052
wherein, O represents the origin of the projection coordinate system, P 'represents the center of the infinitesimal, and a', B ', and C' represent the corresponding points of the three vertexes A, B, C of the triangular patch on the projection plane, respectively.
Calculating corresponding lambda in the projection coordinate system1,λ2,λ3Namely:
Figure BDA0003058176080000053
wherein the content of the first and second substances,orP′＝[xp yp h]Ta component array of a vector from the origin O of the projection coordinate system to the center P' of the infinitesimal under the projection coordinate system is represented,orA′＝[xa ya h]T、orB′＝[xb yb h]T、orC′＝[xc yc h]Tand respectively representing the component arrays of the vectors from the origin O of the projection coordinate system to A ', B ' and C ' on the projection plane under the projection coordinate system.
When min (lambda)1,λ2,λ3) And when the number of the infinitesimal elements is more than or equal to 0, the infinitesimal elements are positioned inside the projection of the triangular patch, and on the contrary, the infinitesimal elements are positioned outside the projection of the triangular patch.
Assuming that the corresponding point of the infinitesimal on the triangular patch ABC is P, the Z-axis component of the P point in the projection coordinate system can be calculated by the following formula:
Figure BDA0003058176080000061
the infinitesimal may be more than the projection of a point on one patch, wherein the patch corresponding to the maximum Z-axis component is the illuminated surface of the infinitesimal, the corresponding infinitesimal on the patch is determined as the illuminated surface, and the corresponding infinitesimal on the other patch is determined as the occlusion.
And step 3: and determining the sunlight pressure moment on the spacecraft.
The component array of the solar radiation pressure on the infinitesimal dA on the panel under a projection coordinate system is as follows:
Figure BDA0003058176080000062
wherein, P is approximately equal to 4.56 multiplied by 10-6N/m2Representing the radiation pressure, dA representing the area of the irradiated infinitesimal, γ representing the angle between the normal vector outside the patch and the direction of the sun, ρaDenotes the absorption proportionality coefficient, psDenotes the specular reflection coefficient, pdRepresents a diffuse reflection coefficient and satisfies ρa+ρs+ρd＝1。
The component array of the sunlight pressure moment borne by the spacecraft in the body coordinate system is as follows:
Tsrp＝Rbo∑ori ×dF (15)
wherein the content of the first and second substances,oria component array of the vector representing the origin of the projection coordinate system to the infinitesimal on the patch under the projection coordinate system,ori ×to representoriIs defined as:
Figure BDA0003058176080000063
and 4, step 4: and establishing an analytical expression of the sunlight pressure moment applied to the spacecraft. The method comprises the following specific steps:
step 4.1: the optical pressure moment analytic expression of the invention is based on the following hypothesis
Assume that 1: the spacecraft is structurally characterized in that a central body is provided with two symmetrically distributed solar sailboards, the central body is a uniform and symmetrical hexahedron, and the centroid of the central body coincides with the mass center.
Assume 2: the attitude angle of the spacecraft is in a small range, and the central body of the spacecraft is shielded from the sailboard very little and can be ignored.
Step 4.2: establishing an analytic expression of the sunlight pressure moment borne by the central body of the spacecraft
Based on the assumption of step 4.1, the centroid and the mass center of the spacecraft center body coincide, and the method comprises the following steps:
br1＝bn1＝[1 0 0]T,br2＝bn2＝[0 1 0]T,br3＝bn3＝[0 0 1]T (16)
wherein the content of the first and second substances,brk(k is 1,2,3) represents the component array of the vector from the origin of the body coordinate system to the center of mass of the central body patch under the body coordinate system,bnkand (k is 1,2 and 3) represents a component array of the out-of-patch normal vector in the body coordinate system.
Component array of sun direction under body coordinate systembs can be expressed as:
Figure BDA0003058176080000071
the analytical expression of the light pressure moment applied to the central body of the spacecraft in the body coordinate system is as follows:
Figure BDA0003058176080000072
therefore, based on the assumption of step 4.1, the solar pressure moment of the central body may not be considered.
Step 4.3: establishing an analytical expression of sunlight pressure moment borne by spacecraft sailboards
Based on the assumption of step 4.1, the two sailboards of the spacecraft are symmetrically distributed, and the method comprises the following steps:
br1＝-br2 (19)
bnk＝Rbak aknk＝Rbak[0 0 1]T＝[sinβk 0 cosβk]T (20)
wherein the content of the first and second substances,brk(k is 1,2) is a component array of a vector from the origin of the body coordinate system to the center of mass of the windsurfing board under the body coordinate system,bnkand (k is 1,2) represents the component array of the outer normal vector of the windsurfing board patch in the body coordinate system.
The analytical expression of the light pressure moment borne by the spacecraft sailboard in the body coordinate system is as follows:
Figure BDA0003058176080000073
Figure BDA0003058176080000081
the analytic expression of the sunlight pressure moment applied to the sailboards is analyzed, and when the rotation angles of the two sailboards are equal, namely beta is obtained1＝β2When the sun pressure moment generated by the sailboard is zero, i.e. Ts_srpWhen the turning angles of the two sailboards are not equal, i.e. beta1≠β2While being installed in the main system YbThe windsurfing of the shaft will take place around XbAnd ZbThe moment of the shaft.
The invention provides a method for determining sunlight pressure moment aiming at a spacecraft on a sun center orbit and based on a sunlight pressure model, and the method has the main advantages that:
1) the method for determining the light pressure moment provided by the invention judges whether all parts of the spacecraft are mutually shielded by utilizing the properties of the convex set, the principle is simple and easy to understand, and the calculation precision is higher.
2) The method for determining the light pressure moment has universality, and almost all sun-center orbit spacecrafts can calculate the sunlight pressure moment applied to the spacecrafts by the method.
3) The invention provides an analytic expression of the sunlight pressure moment aiming at the spacecraft configuration of adding two symmetrically distributed sailboards to the central body, under the condition of small attitude of the spacecraft, the accuracy of calculating the sunlight pressure moment by using the expression basically cannot be reduced, and the calculation time can be effectively reduced.
[ description of the drawings ]
Fig. 1 is a schematic structural diagram of a spacecraft.
Fig. 2 is a schematic view of each coordinate system.
FIG. 3 is a schematic view of the exposure of a micro element.
Fig. 4 is a flow chart of sunlight pressure moment calculation.
[ detailed description ] embodiments
The following will specifically describe the implementation process of the present invention by taking a spacecraft of a certain type of the sun orbit as an example, as shown in fig. 1 to 4. The parameters of the spacecraft are as follows:
the spacecraft is composed of a central rigid body and two symmetrically distributed sailboards, and the central rigid body and the sailboards are all homogeneous hexahedrons. The size of the central rigid body is 50 × 25 × 20cm3The size of the sailboard is 80 multiplied by 25 multiplied by 1cm3The coordinates of the two solar panels at the installation point are respectively (0, ± 21,0) cm under the central body mechanical coordinate system. The orbit of the spacecraft is a circular orbit and is positioned in the ecliptic plane of the solar center, and the distance from the spacecraft to the solar center is an astronomical unit. The absorption proportionality coefficient of the central rigid body and the sailboard is rhoa0.75, and a specular reflection coefficient ρs0.25, diffuse reflectance is ρd0. The attitude angle of the spacecraft is
Figure BDA0003058176080000093
Theta is 10 degrees, psi is 9 degrees, and the rotation angles of the two sailboards are respectively beta1＝5°，β2At 8 deg.. As shown in fig. 4, the following describes the specific implementation process:
1. and establishing a projection coordinate system and obtaining a component array of the spacecraft under the projection coordinate system. The method specifically comprises the following steps:
1.1 defines the coordinate system: and (4) defining a sun center inertia coordinate system, a sun center orbit coordinate system, a body coordinate system and a sailboard fixed connection coordinate system according to the step 1.1.
1.2 rotation matrix calculation between coordinate systems
According to attitude angle of spacecraft
Figure BDA0003058176080000094
Theta, psi, sailboard angle beta1,β2Calculating the coordinates f of the orbit of the sun center according to the step 1.2oBody coordinate system fbCoordinate system f fixed with sailboardakA rotation matrix therebetween, i.e. a centroid orbital coordinate system foTo the body coordinate system fbA rotation matrix of RboBody coordinate system fbOrbital coordinate system f to the center of the sunoA rotation matrix of RobDefine a body coordinate system fbCoordinate system f for fixing to sailboardakA rotation matrix of RakbSailboard fixed connection coordinate system fakTo the body coordinate system fbA rotation matrix of RbakThe result of the calculation is
Figure BDA0003058176080000091
Figure BDA0003058176080000092
Rob＝R′bo,Rbak＝R′akb (24)
1.3 coordinate transformation of spacecraft infinitesimal
Selecting a component array of a sun direction vector (a vector of an origin point of a body coordinate system pointing to the sun center) in a projection coordinate system of a sun center orbit coordinate systemos is:
os＝[0 0 1]T (25)
obtaining coordinate data of mass infinitesimal of each component according to the structure and the size of the spacecraft, converting the coordinate data into a projection coordinate system, and dividing the coordinate data into a central body and a sailboard, wherein the expressions are respectively as follows:
orbi＝Rob brbi (26)
orbj＝Rob(brbak+Rbak akrakj) (27)
wherein the content of the first and second substances,brbiandorbirespectively representing the origin o of the body coordinate systembThe component arrays of the vector to the central body mass element under the body coordinate system and the projection coordinate system,akrakjindicating origin o of sailboard fixed coordinate systemakThe vector to the quality infinitesimal of the sailboard is a component array under the fixedly connected coordinate system of the sailboard,orbjrepresenting origin o of body coordinate systembA component array of vectors to the sail panel mass infinitesimal under a projection coordinate system,brbakrepresenting origin o of body coordinate systembTo the origin o of the coordinate system of the attachment of the sailboardakThe component array of the vector of (1) in the body coordinate system.
2. And (4) shielding judgment is carried out on the spacecraft to obtain an effective irradiation unit. The method comprises the following specific steps:
2.1 Elimination of the illuminated backside to obtain an illuminated surface
Dividing the surface of the spacecraft into a plurality of triangular patches by using finite element analysis software, and solving the component array of the normal vector of the patches in the projection coordinate system according to the component array of the vertices of the triangular patches in the projection coordinate systemon0The expression is:
Figure BDA0003058176080000101
wherein A, B, C respectively represent the three vertices of a triangular patch,orA、orB、orCand the vector matrixes from the origin of the projection coordinate system to the three vertexes of the triangular patch under the projection coordinate system are respectively expressed, and the | | r | | represents two norms of r.
Component array of patch external normal vector (normal vector pointing to outer side of spacecraft) in projection coordinate systemon is corrected through points on a triangular patch, and the expression is as follows:
on＝sign(orP·on0)on0 (29)
wherein the content of the first and second substances,orPand the vector from the origin of the projection coordinate system to the P point on the triangular surface plate is represented as a component array under the projection coordinate system, and sign (#) is a symbolic function.
By a function H (os·on) determining the surface to be irradiated:
Figure BDA0003058176080000111
wherein the content of the first and second substances,onzto representoZ-axis component of n, H: (os·on) — 1 denotes that the patch is irradiated, H: (os·on) — 0 indicates that the patch is occluded.
2.2 determination of occlusion between spacecraft Components
Projecting all illuminated patches onto a projection surface, wherein the projection surface equation is as follows:
z＝h＝1m (31)
the projection pattern of the illumination surface is subjected to infinitesimal division, and if the infinitesimal is positioned in the projection of the surface patch, a positive number lambda exists1,λ2,λ3Such that:
Figure BDA0003058176080000112
wherein, O represents the origin of the projection coordinate system, P 'represents the center of the infinitesimal, and a', B ', and C' represent the corresponding points of the three vertexes A, B, C of the triangular patch on the projection plane, respectively.
Calculating corresponding lambda in the projection coordinate system1,λ2,λ3Namely:
Figure BDA0003058176080000113
wherein the content of the first and second substances,orP′＝[xp yp h]Ta component array of a vector from the origin O of the projection coordinate system to the center P' of the infinitesimal under the projection coordinate system is represented,orA′＝[xa ya h]T、orB′＝[xb yb h]T、orC′＝[xc yc h]Tand respectively representing the component arrays of the vectors from the origin O of the projection coordinate system to A ', B ' and C ' on the projection plane under the projection coordinate system.
Remains to satisfy the inequality min (lambda)1,λ2,λ3) A patch of ≧ 0, which may be a plane whose infinitesimal is illuminated.
Assuming that the corresponding point of the infinitesimal on the triangular patch ABC is P, the Z-axis component of the P point in the projection coordinate system can be calculated by the following formula:
Figure BDA0003058176080000121
the patch corresponding to the maximum Z-axis component is the irradiation surface of the infinitesimal, the infinitesimal corresponding to the patch is judged as the irradiation surface, and the infinitesimal corresponding to the other patches is judged as the shielding.
3. And determining the sunlight pressure moment on the spacecraft.
The component array of the solar radiation pressure on the infinitesimal dA on the panel under a projection coordinate system is as follows:
Figure BDA0003058176080000122
wherein, P is approximately equal to 4.56 multiplied by 10-6N/m2Representing the radiation pressure, dA representing the area of the irradiated infinitesimal, γ representing the angle between the normal vector outside the patch and the direction of the sun, ρaDenotes the absorption proportionality coefficient, psDenotes the specular reflection coefficient, pdRepresents a diffuse reflection coefficient and satisfies ρa+ρs+ρd＝1。
The component array of the sunlight pressure moment borne by the spacecraft in the body coordinate system is as follows:
Figure BDA0003058176080000123
wherein the content of the first and second substances,oria component array of the vector representing the origin of the projection coordinate system to the infinitesimal on the patch under the projection coordinate system,ori ×to representoriIs defined as a cross-multiplication matrix of
Figure BDA0003058176080000131
4. And establishing an analytical expression of the sunlight pressure moment applied to the spacecraft. The method comprises the following specific steps:
4.1 the light pressure torque analytic expression of the invention is based on the following assumptions
Assume that 1: the spacecraft is structurally characterized in that a central body is provided with two symmetrically distributed solar sailboards, the central body is a uniform and symmetrical hexahedron, and the centroid of the central body coincides with the mass center.
Assume 2: the attitude angle of the spacecraft is in a small range, and the central body of the spacecraft is shielded from the sailboard very little and can be ignored.
4.2 establishing an analytic expression of the sunlight pressure moment borne by the central body of the spacecraft
And (3) substituting the spacecraft parameters into the analytical expression in the step 4.2 for calculation, wherein the analytical expression and the specific size of the light pressure moment borne by the central body of the spacecraft under the body coordinate system are as follows:
Figure BDA0003058176080000132
4.3 establishing an analytic expression of the sunlight pressure moment borne by the spacecraft sailboard
And (4) substituting the spacecraft parameters into the analytical expression in the step 4.3 for calculation, wherein the analytical expression and the specific size of the light pressure moment borne by the spacecraft sailboard in the body coordinate system are as follows:
Figure BDA0003058176080000133
Figure BDA0003058176080000141
the specific magnitude of the sunlight pressure moment borne by the spacecraft can be obtained through solving through the steps. Comparing the sunlight pressure moment obtained by the step 3 and the calculation of the analytical expression, calculating the X-ray winding by using the analytical expressionbAnd ZbThe optical pressure moment of the shaft is within 7 percent and around YbOptical pressure to moment ratio of axis about XbAnd ZbThe light pressure moment of the shaft is smaller by 4 orders of magnitude, and it is reasonable to regard the light pressure moment as zero in the analytical expression, which shows that the obtained solar light pressure moment analytical expression has certain precision.

Claims (3)

1. A sun light pressure moment determination method for a sun-center orbit spacecraft is characterized by comprising the following steps: the method comprises the following steps:
step 1: establishing a projection coordinate system and obtaining a component array of the spacecraft under the projection coordinate system, wherein a centroid orbit coordinate system is taken as the projection coordinate system;
step 2: shelter from the judgement to the spacecraft, obtain effective irradiation unit, mainly include: judging whether the micro elements are illuminated or not, eliminating mutual shielding among the parts and obtaining the micro elements which are actually illuminated;
and step 3: determining the sunlight pressure moment on the spacecraft;
and 4, step 4: establishing an analytical expression of the sunlight pressure moment applied to the spacecraft so as to quickly obtain the magnitude of the sunlight pressure moment:
the optical pressure moment analytic expression is based on the following assumptions:
assume that 1: the spacecraft is structurally characterized in that a central body is provided with two symmetrically distributed solar sailboards, the central body is a uniform and symmetrical hexahedron, and the centroid of the central body is coincided with the centroid of the central body;
assume 2: the attitude angle of the spacecraft is in a small range, and the mutual shielding between the central body of the spacecraft and the sailboard is very small and can be ignored;
obtaining:
the analytical expression of the light pressure moment applied to the central body of the spacecraft in the body coordinate system is as follows:
Figure FDA0003058176070000011
the analytical expression of the light pressure moment borne by the spacecraft sailboard in the body coordinate system is as follows:
Figure FDA0003058176070000012
Figure FDA0003058176070000021
the analytic expression of the sunlight pressure moment applied to the sailboards is analyzed, and when the rotation angles of the two sailboards are equal, namely beta is obtained1＝β2When the sun pressure moment generated by the sailboard is zero, i.e. Ts_srpWhen the turning angles of the two sailboards are not equal, i.e. beta1≠β2While being installed in the main system YbThe windsurfing of the shaft will take place around XbAnd ZbThe moment of the shaft.
2. The solar pressure moment determination method for the sun-centered orbit spacecraft according to claim 1, characterized in that: wherein, the selection of the centroid orbit coordinate system in the step 1 is a projection coordinate system, which specifically comprises the following steps: component array of sun direction vector under projection coordinate systemos is:
os＝[0 0 1]T
converting coordinate data of mass infinitesimal of each component of the spacecraft into a projection coordinate system, and dividing the coordinate data into a central body and a sailboard, wherein the expressions are respectively as follows:
orbi＝Rob brbi
orbj＝Rob(brbak+Rbak akrakj)
wherein the content of the first and second substances,brbiandorbirespectively representing the origin o of the body coordinate systembThe component arrays of the vector to the central body mass element under the body coordinate system and the projection coordinate system,akrakjindicating origin o of sailboard fixed coordinate systemakThe vector to the quality infinitesimal of the sailboard is a component array under the fixedly connected coordinate system of the sailboard,orbjrepresenting origin o of body coordinate systembA component array of vectors to the sail panel mass infinitesimal under a projection coordinate system,brbakrepresenting origin o of body coordinate systembTo the origin o of the coordinate system of the attachment of the sailboardakThe component array of the vector of (1) in the body coordinate system.
3. The solar pressure moment determination method for the sun-centered orbit spacecraft according to claim 1, characterized in that: wherein, the step 2 specifically comprises:
step 2.1: eliminating the back side to obtain the irradiated surface
Dividing the surface of the spacecraft into a plurality of triangular patches by using finite element analysis software, and solving the component array of the normal vector of the patches in the projection coordinate system according to the component array of the vertices of the triangular patches in the projection coordinate systemon0The expression is:
Figure FDA0003058176070000031
wherein A, B, C respectively represent the three vertices of a triangular patch,orA、orB、orCrespectively representing a component array of vectors from an original point of a projection coordinate system to three vertexes of a triangular patch under the projection coordinate system, | | r | | represents two norms of r;
component array of patch external normal vector under projection coordinate systemon is corrected through points on a triangular patch, and the expression is as follows:
on＝sign(orP·on0)on0
wherein the content of the first and second substances,orPrepresenting a component array of a vector from an origin of a projection coordinate system to a point P on the triangular surface under the projection coordinate system, wherein sign (#) is a sign function;
by a function H (os·on) determining the surface to be irradiated:
Figure FDA0003058176070000032
wherein the content of the first and second substances,onzto representoZ-axis component of n, H: (os·on) — 1 denotes that the patch is irradiated, H: (os·on) ═ 0 represents that the patch is occluded;
step 2.2: occlusion determination between spacecraft components
Projecting all illuminated patches onto a projection surface, wherein the projection surface equation is as follows:
z＝h
the projection pattern of the illumination surface is subjected to infinitesimal division, and if the infinitesimal is positioned in the projection of the surface patch, a positive number lambda exists1,λ2,λ3Such that:
Figure FDA0003058176070000041
wherein, O represents the origin of the projection coordinate system, P 'represents the center of the infinitesimal, A', B 'and C' respectively represent the corresponding points of three vertexes A, B, C of the triangular patch on the projection plane;
calculating corresponding lambda in the projection coordinate system1,λ2,λ3Namely:
Figure FDA0003058176070000042
wherein the content of the first and second substances,orP′＝[xp yp h]Ta component array of a vector from the origin O of the projection coordinate system to the center P' of the infinitesimal under the projection coordinate system is represented,orA′＝[xa ya h]T、orB′＝[xb yb h]T、orC′＝[xc yc h]Trespectively representing the component arrays of the vectors from the origin O of the projection coordinate system to A ', B ' and C ' on the projection plane under the projection coordinate system;
when min (lambda)1,λ2,λ3) When the number of the infinitesimal elements is more than or equal to 0, the infinitesimal elements are positioned inside the projection of the triangular patch, and on the contrary, the infinitesimal elements are positioned outside the projection of the triangular patch;
assuming that the corresponding point of the infinitesimal on the triangular patch ABC is P, the Z-axis component of the P point in the projection coordinate system can be calculated by the following formula:
Figure FDA0003058176070000043
the infinitesimal may be more than the projection of a point on one patch, wherein the patch corresponding to the maximum Z-axis component is the illuminated surface of the infinitesimal, the corresponding infinitesimal on the patch is determined as the illuminated surface, and the corresponding infinitesimal on the other patch is determined as the occlusion.
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