CN107944094B - Method and system for determining projection area of spacecraft with complex appearance - Google Patents
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Abstract
A method and a system for determining the projection area of a spacecraft with a complex shape develop a method for calculating the projection area of the spacecraft with the complex shape along any direction, which has better robustness and universality, by using the thought of Monte Carlo technology in statistics and combining the basic ray and triangle intersection theory in computational geometry. Firstly, constructing a cuboid box which just surrounds the outer surface of the spacecraft, wherein one surface of the cuboid box is vertical to the projection direction; then, determining a boundary rectangle for generating the test particles, wherein the plane of the boundary rectangle is vertical to the projection direction and is positioned at the upstream of the surrounding box; thirdly, generating test particles on the boundary rectangle, tracking the motion track of the test particles, judging whether the track is intersected with the surface of the spacecraft, and if so, increasing the number of the intersected test particles by 1; and finally, repeating the previous step until the total number of the test particles is large enough to ensure that the calculation result is converged, and counting the projection area of the spacecraft according to the number of the intersected test particles and the total number of the generated test particles.
Description
Technical Field
The invention relates to a method and a system for determining the projection area of a spacecraft with a complex appearance, and belongs to the technical field of aerodynamic characteristic design and attitude orbit control of aircrafts.
Background
In recent years, due to the requirement of accurate measurement of gravity field and steady-state ocean circulation, the ultra-low earth orbit (200- & lt 500km) spacecraft gradually shows wide application prospect, however, the prerequisite for realizing accurate measurement of gravity gradient is accurate calculation of aerodynamic resistance of low-orbit satellites. The aerodynamic drag is mainly determined by the local atmospheric density, the drag coefficient and the projected area of the satellite along the motion direction. The local atmospheric density is generally given by an atmospheric model, the aerodynamic resistance coefficient can be consulted with a database, and the problem to be solved is to calculate the projection area of the aerodynamic resistance coefficient along the movement direction.
Recently, solar sail detectors have shown great potential in the field of deep space exploration because they take advantage of the sunlight pressure to gain impetus and do not need to carry large quantities of propellant. Although the solar light pressure is small, continuous acceleration allows the detector to reach a considerable speed, eventually 5-10 times the speed of a conventional spacecraft. The attitude and trajectory control system of the solar sail detector requires the input of solar pressure, which is related to the solar flux, solar sail surface reflectivity, and projected area along the direction of the light. The solar flux is a physical constant, the reflectivity is a material attribute, the solar flux can be obtained by consulting a relevant manual or experimental measurement, and the calculation of the sunlight pressure is summarized as the calculation of the projection area of the solar sail along the light direction.
In addition, an important part in the design and risk assessment of a spacecraft protection system is the estimation of the collision probability of the micrometeoroid or space debris and spacecraft components, and the premise is to provide the projection area of the spacecraft and each component thereof in a given threat attack direction. Meanwhile, the projection area of the satellite in a certain direction is more directly a necessary input parameter for attitude control, for example, a Sun-aiming (Sun-pointing) attitude mode needs to input the projection area of the satellite in the sunlight direction, and a minimum-drag or maximum-drag attitude mode needs to identify and calculate the minimum or maximum projection area of the satellite.
The method for generating the projection of the geometric entity along a certain direction is called as an occlusion algorithm in the field of computer graphics, is an intuitive numerical method for calculating the projection area of the geometric entity, and is continuously researched and perfected so far. Currently, the projection algorithms widely used in computer graphics are ray casting and ray tracing methods: the light projection method calculates the intersection point of the light emitted from the light source and the surface of the geometric solid, identifies a visible surface (a non-visible surface is a backlight surface) through the minimum distance, and then projects the visible surface by adopting a polygon projection algorithm to generate a projected image of the geometric solid; the ray tracing method considers the effects of ray scattering and reflection on the basis of a ray projection method.
However, no matter the calculation of the atmospheric resistance of the low orbit satellite and the light pressure of the solar sail detector, the protection design and risk assessment of the spacecraft and the attitude control of the spacecraft, the input of the projection area of the spacecraft (component) is only needed, and obviously, the time and the labor are consumed by generating a projection image by a computer graphics method and then calculating the projection area. Foreign researchers develop an analytic method for calculating the projection area of the spacecraft in any direction based on the convex polygon theory. Because each process is realized in the form of analytic solution, the method has high calculation efficiency. However, after the spacecraft with a complex shape performs polygon discretization, the projected polygons of the spacecraft are inevitably intersected pairwise or even three or more polygons are intersected simultaneously, so that the calculation of the intersected area of the projected polygons is extremely difficult or even impossible. Moreover, the nature of the analysis results in poor robustness and versatility, and in some extreme cases, the rounding errors inherent in computers can lead to erroneous computation results. The more complex the spacecraft profile, the greater the likelihood of extreme conditions. Therefore, the analysis method is highly efficient, but is difficult to be applied to space engineering practice.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method and the system for determining the projection area of the spacecraft with the complex appearance along any direction overcome the defects of the prior art, and the problem that the projection area of the spacecraft with the complex appearance cannot be calculated in the prior art is solved.
The technical solution of the invention is as follows:
a method for determining the projected area of a spacecraft with a complex shape comprises the following steps:
(1) constructing a projection coordinate system Oxyz;
(2) constructing a cuboid box surrounding the outer surface of the spacecraft, wherein 3 mutually vertical edges of the cuboid are respectively parallel to an x axis, a y axis and a z axis;
(3) determining a bounding rectangle from which the test particle is generated;
(4) randomly generating test particles in the boundary rectangle given in the step (3), and giving initial coordinates r of the test particles in a projection coordinate system0；
(5) Judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft: if not, directly turning to the step (6); if the intersection is detected, the number Q of the intersection test particles is increased by 1, and then the step (6) is continuously executed;
(6) judging whether the total number M of the generated test particles is smaller than a preset value, if so, turning to the step (4), otherwise, continuing to execute the step (7);
(7) and counting the projection area of the spacecraft according to the number Q of the intersected test particles and the total number M of the generated test particles.
Constructing a projection coordinate system Oxyz, which specifically comprises the following steps:
(1.1) firstly, constructing an organism coordinate system OXYZ, wherein the origin of coordinates is the mass center O, X, Y of the spacecraft, and the Z axis coincides with the inertia main axis of the spacecraft;
(1.2) constructing a projection coordinate system Oxyz according to an organism coordinate system OXYZ, wherein the origin of the projection coordinate system is positioned at the mass center O of the spacecraft, the positive direction of a z-axis is the projection direction, and the projection of Oz on a plane is OzPOy lies in the XOY plane and is perpendicular to OzPOx is determined by the right hand rule.
The step (2) is to construct a cuboid box surrounding the outer surface of the spacecraft, and 6 surfaces of the cuboid are expressed as projection coordinate system
The surface of the spacecraft is dispersed by triangular units, N is the number of the triangular units on the surface of the spacecraft, (x)i,yi,zi),i∈[1,N]The coordinates of the triangle unit nodes in the projection coordinate system.
The boundary rectangle in the step (3) is perpendicular to the projection direction and is positioned at the upstream of the cuboid box, and the coordinates of the boundary rectangle meet the requirement
Initial coordinate r in step (4)0(x0,y0,z0) The method specifically comprises the following steps:
in the formula, R1、R2Are random numbers uniformly distributed in the interval of (0, 1).
Judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft in the step (5), and specifically comprising the following steps of:
(5.1) calculating the motion trail of the test particle ray: according to the initial position coordinates r of the test particles0(x0,y0,z0) And the projection direction to obtain a ray parameter equation of
Wherein t is a time parameter;
(5.2) calculating an equation of the plane where the triangular unit is located: let the coordinate of any vertex of triangle ABC be (x)1,y1,z1) The surface normal vector is n ═ n (n)1,n2,n3) Then the equation of the plane in which it is located is
n·(x-x1,y-y1,z-z1)＝0；
(5.3) judging whether the ray track of the test particle intersects with the plane of the triangular unit: simultaneous ray parameter equation and equation of triangle plane
If n is3If 0, the plane is parallel to the ray, the two do not intersect, otherwise, the result is obtained
If t is less than or equal to 0, the ray does not intersect with the plane and further does not intersect with the triangle unit, if t is more than 0, the ray enters
Step (5.4) further judging whether the intersection point is in the triangle ABC;
(5.4) substituting the value of the parameter t into the ray parameter equation to obtain the coordinate (x) of the intersection point PP,yP,zP) Is composed of
Order to
If at the same time satisfy
And if the intersection point P is inside the triangle ABC, the ray motion trail of the test particle is intersected with the triangle unit on the surface of the spacecraft, otherwise, the intersection point is outside the triangle ABC, and the ray motion trail is not intersected with the triangle unit.
The preset value in the step (6) is more than or equal to 106。
The projected area A of the spacecraft is counted in the step (7)PThe concrete formula is
AP＝(xmax-xmin)(ymax-ymin)(Q/M)
Wherein M is the total number of the generated and tracked test particles, and Q is the number of the test particles of which the motion trail intersects with the surface of the spacecraft.
The value range 10 of the preset value6～108。
A system for determining projected area of a complex-shaped spacecraft, comprising:
a coordinate system construction module: used for constructing a projection coordinate system Oxyz;
a box construction module: the device is used for constructing a cuboid box surrounding the outer surface of the spacecraft, and 3 edges of the cuboid are respectively parallel to an x axis, a y axis and a z axis;
a bounding rectangle generation module: for determining a bounding rectangle from which the test particle is generated;
test particle generation module: for randomly generating test particles in the boundary rectangle determined by the boundary rectangle generating module, giving the initial coordinates r of the test particles in the projection coordinate system0；
An intersection judgment module: the system is used for judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft or not and counting the number Q of intersecting test particles;
projection area calculation module: and the device is used for counting the projection area of the spacecraft according to the number Q of the intersected test particles counted by the intersection judging module and the total number M of the generated test particles.
Compared with the prior art, the invention has the advantages that:
(1) the existing method for calculating the projection area of the spacecraft with the complex shape is time-consuming and labor-consuming either by generating a projection image by a computer graphics method and then calculating the projection area, or by adopting an analytic method based on a convex polygon theory, the generality and the robustness are poor and the method cannot be applied to aerospace engineering. Based on the method, the thought of the Monte Carlo technology in statistics is used for reference, and the basic ray and triangle intersection theory in computational geometry is combined, so that the method for calculating the projection area of the spacecraft with the complex shape along any direction is developed.
(2) Compared with a projection algorithm of computer graphics, the method has the advantages of high calculation speed and low storage requirement, and compared with an analysis method based on a convex polygon theory, the method has good robustness and universality and has the capability of processing any complex engineering shape. In addition, the calculation time of the method of the invention is in a linear relation with the increase of the calculation scale, the problem complexity and the space dimension, and the method is an ideal method for calculating the projection area of the spacecraft with the complex shape.
Description of the drawings:
FIG. 1: a method flow diagram of the invention;
FIG. 2: a body coordinate system and a projection coordinate system schematic diagram;
FIG. 3: a single-sided circular flat plate schematic diagram (a) and discretization of triangular units thereof (b);
FIG. 4: comparing the calculation result with the theoretical result of the single-sided circular flat plate;
FIG. 5: a SAMSON satellite model schematic diagram;
FIG. 6: the variation of the projected area of the SAMSON satellite along with the posture thereof, wherein FIG. 6(a) is a three-dimensional distribution diagram, and FIG. 6(b) is an isovalent curve;
FIG. 7: schematic diagram of the gote satellite model, wherein fig. 7(a) is a head direction view, and fig. 7(b) is a tail direction view;
FIG. 8: the GOCE satellite projection area changes along with the attitude; in this case, fig. 8(a) is a three-dimensional distribution diagram, and fig. 8(b) is an iso-curve.
Detailed Description
According to the requirement of calculating the projection area of the existing spacecraft with the complex appearance, the invention provides a method for calculating the projection area of the spacecraft with the complex appearance along any direction by using the thought of Monte Carlo technology in statistics and combining the basic ray and triangle intersection theory in computational geometry.
Firstly, constructing a cuboid box which just surrounds the outer surface of the spacecraft, wherein one surface of the cuboid box is vertical to the projection direction; then, determining a boundary rectangle for generating the test particles, wherein the plane of the boundary rectangle is vertical to the projection direction and is positioned at the upstream of the surrounding box; generating test particles in the boundary rectangle, giving position coordinates of the test particles, tracking the motion track of the test particles, judging whether the track is intersected with the surface triangular unit of the spacecraft, if so, increasing the number of the intersected test particles by 1, and if not, performing the next step; and finally, repeating the previous step until the total number of the test particles is large enough to ensure that the calculation result is converged, and counting the projection area of the spacecraft according to the number of the intersected test particles and the total number of the generated test particles.
As shown in fig. 1, the specific steps are as follows:
(1) constructing a body coordinate system B and a projection coordinate system P, and specifically realizing the following processes:
and the origin of coordinates of the body coordinate system B is positioned at the mass center O, X, Y of the spacecraft, and the Z axis is coincided with the inertia main shaft of the spacecraft. The origin of the projection coordinate system P is also positioned at the centroid O of the spacecraft, and the z axis of the projection coordinate system P is coincident with the projection direction, namely the projection direction is Oz axisLet the projection of Oz on the plane be OzPOy lies in the XOY plane and is perpendicular to OzPOx is determined by the right-hand rule,
as shown in fig. 2. The inclination angle of the Oz and XOY planes is defined as declination delta in the range of delta E [ -pi/2, using the terminology of spacecraft orbital mechanics or astronomy]，OzPThe angle to OX is defined as the right ascension alpha, which ranges from alpha e [0,2 pi ]. Unless otherwise specified, the coordinates or vectors in the following are quantities in the projected coordinate system P.
(2) And constructing a cuboid box just surrounding the outer surface of the spacecraft, wherein 3 mutually vertical edges of the cuboid are respectively parallel to the x axis, the y axis and the z axis of the projection coordinate system. Generally, the surface of a spacecraft with a complex shape is dispersed by triangular units, the number of the triangular units on the surface is N, and the coordinates of unit nodes in a projection coordinate system are (x)i,yi,zi),i∈[1,N]Then 6 faces of the rectangular parallelepiped case are defined by the following formula
(3) The bounding rectangle that produces the test particle is determined. The plane of the bounding rectangle is perpendicular to the projection direction and is located upstream of the bounding box, and the coordinates of the bounding rectangle satisfy
(4) Randomly generating test particles by the boundary rectangle given in the step (3), and giving the positions of the test particles in the projection coordinate system and the initial coordinate r0(x0,y0,z0) Is composed of
R1、R2Are random numbers uniformly distributed in the interval of (0, 1).
(5) Judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft: if not, directly turning to the step (6); if so, the number Q of the intersected test particles is incremented by 1, and then the step (6) is continuously executed. The initial value of Q is 0; the specific implementation process is as follows:
and (5.1) calculating the motion trail of the test particle ray. According to the initial position coordinates r of the test particles0(x0,y0,z0) And projection direction, easily obtained as a parametric equation
And (5.2) calculating an equation of the plane where the triangular unit is located. Let the coordinate of any vertex of triangle ABC be (x)1,y1,z1) The surface normal vector is n ═ n (n)1,n2,n3) Then the equation of the plane in which it is located is
n·(x-x1,y-y1,z-z1)＝0
And (5.3) judging whether the test particle ray track intersects with the plane where the triangular unit is located. Simultaneous ray parameter equation and equation of triangle plane
If n is3If 0, the plane is parallel to the ray, the two clearly do not intersect, otherwise it is easy to find
If t is less than or equal to 0, the ray does not intersect with the plane and does not intersect with the triangle unit naturally, otherwise, whether the intersection point is inside the triangle ABC needs to be further judged.
(5.4) if the motion trail of the test particle ray intersects with the plane of the triangle ABC, judging whether the intersection point P is inside the triangle ABC. The value of the parameter t is substituted into a ray parameter equation, so that the method is easy to realizeObtaining the coordinates (x) of the point of intersection PP,yP,zP) Is composed of
Order to
If at the same time satisfy
And if the intersection point P is inside the triangle ABC, the ray motion trail of the test particle is intersected with the triangle unit on the surface of the spacecraft, otherwise, the intersection point is outside the triangle ABC, and the ray motion trail is not intersected with the triangle unit.
(6) And (4) judging whether the total number of the generated and tracked test particles is less than a preset value, if so, turning to the step (4), otherwise, continuing to execute the step (7).
The number of generally tracked test particles is 10 or more6At that time, the projected area starts to be counted. The statistical error and the calculation time are comprehensively considered and can be 106～108An internal value.
(7) And (5) counting the projection area of the spacecraft. Setting the number of generated and tracked test particles as M, wherein the number of the test particles of which the motion trail intersects with the surface of the spacecraft is Q, and setting the projection area A of the spacecraft along the z axis asPIs composed of
AP＝(xmax-xmin)(ymax-ymin)(Q/M)
The statistical error ε is the quotient of the standard deviation σ of the single error distribution and the square root of the total number of test particles, i.e.
Therefore, after a sufficient number of test particles are generated and tracked, the projected area must converge and the statistical error is
The specific solving example of the complex-shape spacecraft projection area calculation is as follows:
firstly, a single-sided circular flat plate with simple appearance and analytic solution in the projection area is considered, so that comparative analysis is facilitated. The schematic diagram of a single-sided circular flat plate, the coordinate system of the body and the projection direction are shown in fig. 3a, the axial direction, the span direction and the normal direction are X, Y and the Z-axis respectively, and the projection axis is the Z-axis. The radius of the circular plate is 1m, and only the situation that the right ascension α is 0 ° needs to be considered due to the axisymmetric characteristic. Therefore, the Z-axis is located on the XOZ plane, the included angle with the X-axis is declination delta, and the included angle with the Z-axis is the complementary angle of declination. The dispersion was carried out using 608 triangular units, as shown in FIG. 3b, and the total number of test particles was 2X 107When the statistical error is
Fig. 4 shows the variation of the projected area of the single-sided plate with declination, which ranges from δ e [0 °,90 ° ], i.e. the projection direction varies from parallel to the plate surface to perpendicular to the plate surface. When the projection direction is parallel to the surface of the flat plate (delta is 90 degrees), the projection area is 0; when the projection direction is vertical to the surface of the flat plate (delta is 90 degrees), the projection area is the area pi of the flat plate; the projected area increases as a sinusoidal function as the projection direction changes from parallel to perpendicular to the plate surface.
For this simple shape, the theoretical solution to the projected area is the product of the area of the plate and the declination sine, i.e.
AP＝πcos(π/2-δ)＝πsinδ
Obviously, the Monte Carlo statistical result of the invention is completely consistent with the theoretical solution, and the reliability of the method is verified.
Then, consider the SAMSON minisatellite of the european space agency, as shown in fig. 5. Table 1 lists SAMSON satellites along several representativesThe projected areas of the directions (declination delta and right ascension alpha) give the calculation results of the invention, reliable literature results and relative errors of the two. When the declination δ is 90 °, the projection direction coincides with the Z axis of the body coordinate system, and therefore the projection area is independent of the right ascension. The total number of test particles was 2X 107Corresponding to a statistical error of
And the engineering requirements are met. As can be seen from the table, the calculation results of the invention are consistent with the data reported in the literature, and the magnitude of the relative error is
The same as the magnitude of the statistical error. Therefore, the Monte Carlo technology provided by the invention is suitable for complex engineering application shapes, has the capability of accurately calculating the projection area of the spacecraft with the complex shape along any direction, and the relative error meets the statistical distribution rule.
FIG. 6 is the projected areas of the SAMSON satellite along different directions, FIG. 6(a) is a three-dimensional distribution diagram of the projected areas, FIG. 6(b) is a corresponding two-dimensional contour diagram, and the variation range of declination is delta epsilon-90 degrees and 90 degrees]The variation range of the right ascension is alpha epsilon [0 DEG, 360 DEG ]]. When declination delta is minus 90 degrees, the projection direction is the opposite direction of the Z axis; when the declination delta is equal to 0 degrees, the projection direction is parallel to an XOY plane; when the declination δ is 90 °, the projection direction is the positive Z-axis direction. Obviously, the projection area of the SAMSON satellite along different directions has larger variation range span from the minimum value APmin＝0.03m2To a maximum value APmax＝0.194m2. In addition, when the solar sail is unfolded, the declination, namely the included angle between the projection direction and the XOY plane, has more obvious influence on the projection area. The influence of the right ascension is relatively smaller, which is determined by the geometry of the SAMSON satellites. When the declination delta is close to 0 degrees, the projection area is the smallest, and the influence of the right ascension on the projection area is the largest at the moment; when the declination delta is +/-90 degrees, the projection area is the largest, and the right ascension has no influence on the projection area. Fig. 6 reveals the relationship between the satellite attitude and its projected area, which is a necessary input condition for satellite attitude control.
TABLE 1 projected area under typical attitude of SAMSON satellite
Finally, as an application of the projection area Monte Carlo simulation method in space engineering, a Gravity field of the european space agency and a steady-state Ocean Circulation exploration satellite (gote) are considered, as shown in fig. 7(a) and 7 (b).
FIG. 8 is the projected area of the GOCE satellite along different directions, FIG. 8(a) is the three-dimensional distribution diagram of the projected area, FIG. 8(b) is the corresponding two-dimensional contour diagram, and the variation range of declination is δ e [ -90 DEG, 90 DEG]The variation range of the right ascension is alpha epsilon [0 DEG, 360 DEG ]]. Similar to the SAMON satellite, near declination δ being 0 °, the GOCE projection area is the smallest, and the influence of right ascension on the projection area is the largest at this time; when the declination delta is +/-90 degrees, the projection area is the largest, and the right ascension has no influence on the projection area. However, the shape of the elongated body of a gote satellite, coupled with the large area of the solar wings, results in a larger projected area span along different directions than a SAMSON satellite, from a minimum value aPmin＝0.817m2To a maximum value APmax＝10.273m2. Along with the change of the attitude of the GOCE satellite, the atmospheric resistance and the sunlight pressure change of the GOCE satellite are huge due to the large change range of the projection area of the GOCE satellite, and the power generation efficiency of the solar wing is also changed violently, so that great challenges are provided for the stability, the attitude and the track control of the GOCE satellite. Fig. 8 reveals the relationship between the orientation of the gote satellite and the projection area thereof, which is an input parameter for calculation and monitoring of the power generation amount of the solar wing, prediction of the atmospheric resistance and the sunlight pressure, and is also a necessary condition for satellite orientation and orbit control.
By integrating the above calculation of the projection area of the single-sided circular flat model, the SAMSON satellite and the GOCE satellite, the following conclusions can be obtained: the spacecraft projection area calculation method has the capability of accurately calculating the projection area of any complex spacecraft shape along any direction, has good robustness and universality, can give the relation between the satellite attitude and the projection area thereof, and is an ideal method for calculating the projection area of the complex spacecraft.
The present invention is not disclosed in the technical field of the common general knowledge of the technicians in this field.
Claims (4)
1. A method for determining the projection area of a spacecraft with a complex shape is characterized by comprising the following steps:
(1) constructing a projection coordinate system Oxyz;
(2) constructing a cuboid box surrounding the outer surface of the spacecraft, wherein 3 mutually vertical edges of the cuboid are respectively parallel to an x axis, a y axis and a z axis;
(3) determining a bounding rectangle from which the test particle is generated;
(4) randomly generating test particles in the boundary rectangle given in the step (3), and giving initial coordinates r of the test particles in a projection coordinate system0；
(5) Judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft: if not, directly turning to the step (6); if the intersection is detected, the number Q of the intersection test particles is increased by 1, and then the step (6) is continuously executed;
(6) judging whether the total number M of the generated test particles is smaller than a preset value, if so, turning to the step (4), otherwise, continuing to execute the step (7);
(7) counting the projection area of the spacecraft according to the number Q of the intersected test particles and the total number M of the generated test particles;
constructing a projection coordinate system Oxyz, which specifically comprises the following steps:
(1.1) firstly, constructing an organism coordinate system OXYZ, wherein the origin of coordinates is the mass center O, X, Y of the spacecraft, and the Z axis coincides with the inertia main axis of the spacecraft;
(1.2) constructing a projection coordinate system Oxyz according to an organism coordinate system OXYZ, wherein the origin of the projection coordinate system is positioned at the mass center O of the spacecraft, the positive direction of a z-axis is the projection direction, and the projection of Oz on a plane is OzPOy lies in the XOY plane and is perpendicular to OzPOxygen, nitrogen and oxygen combined deviceDetermining through a right hand rule;
the step (2) is to construct a cuboid box surrounding the outer surface of the spacecraft, and 6 surfaces of the cuboid are expressed as projection coordinate system
The surface of the spacecraft is dispersed by triangular units, N is the number of the triangular units on the surface of the spacecraft, (x)i,yi,zi),i∈[1,N]Coordinates of the triangular unit nodes in a projection coordinate system;
the boundary rectangle in the step (3) is perpendicular to the projection direction and is positioned at the upstream of the cuboid box, and the coordinates of the boundary rectangle meet the requirement
Initial coordinate r in step (4)0(x0,y0,z0) The method specifically comprises the following steps:
in the formula, R1、R2Random numbers which are uniformly distributed in the interval of (0, 1);
judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft in the step (5), and specifically comprising the following steps of:
(5.1) calculating the motion trail of the test particle ray: according to the initial position coordinates r of the test particles0(x0,y0,z0) And the projection direction to obtain a ray parameter equation of
Wherein t is a time parameter;
(5.2) calculating an equation of the plane where the triangular unit is located: let the coordinate of any vertex of triangle ABC be (x)1,y1,z1) The surface normal vector is n ═ n (n)1,n2,n3) Then the equation of the plane in which it is located is
n·(x-x1,y-y1,z-z1)＝0；
(5.3) judging whether the ray track of the test particle intersects with the plane of the triangular unit: simultaneous ray parameter equation and equation of triangle plane
If n is3If 0, the plane is parallel to the ray, the two do not intersect, otherwise, the result is obtained
If t is less than or equal to 0, the ray does not intersect with the plane and further does not intersect with the triangle unit, if t is greater than 0, the step (5.4) is carried out to further judge whether the intersection point is inside the triangle ABC;
(5.4) substituting the value of the parameter t into the ray parameter equation to obtain the coordinate (x) of the intersection point PP,yP,zP) Is composed of
Order to
If at the same time satisfy
If the intersection point P is inside the triangle ABC, the ray motion trail of the test particle is intersected with the triangle unit on the surface of the spacecraft, otherwise, the intersection point is outside the triangle ABC, and the ray motion trail is not intersected with the triangle unit;
the projected area A of the spacecraft is counted in the step (7)PThe concrete formula is
AP＝(xmax-xmin)(ymax-ymin)(Q/M)
Wherein M is the total number of the generated and tracked test particles, and Q is the number of the test particles of which the motion trail intersects with the surface of the spacecraft.
2. The method for determining the projected area of a spacecraft of claim 1, wherein: the preset value in the step (6) is more than or equal to 106。
3. The method for determining the projected area of a spacecraft of claim 1, wherein: the value range 10 of the preset value6～108。
4. A system for determining projected area of a complex geometry spacecraft, comprising:
a coordinate system construction module: used for constructing a projection coordinate system Oxyz;
a box construction module: the device is used for constructing a cuboid box surrounding the outer surface of the spacecraft, and 3 edges of the cuboid are respectively parallel to an x axis, a y axis and a z axis;
a bounding rectangle generation module: for determining a bounding rectangle from which the test particle is generated;
test particle generation module: for randomly generating test particles in the boundary rectangle determined by the boundary rectangle generating module, giving the initial coordinates r of the test particles in the projection coordinate system0；
An intersection judgment module: the system is used for judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft or not and counting the number Q of intersecting test particles;
projection area calculation module: the device is used for counting the projection area of the spacecraft according to the number Q of intersecting test particles counted by the intersection judging module and the total number M of generated test particles;
constructing a projection coordinate system Oxyz, which specifically comprises the following steps:
(1.1) firstly, constructing an organism coordinate system OXYZ, wherein the origin of coordinates is the mass center O, X, Y of the spacecraft, and the Z axis coincides with the inertia main axis of the spacecraft;
(1.2) constructing a projection coordinate system Oxyz according to an organism coordinate system OXYZ, wherein the origin of the projection coordinate system is positioned at the mass center O of the spacecraft, the positive direction of a z-axis is the projection direction, and the projection of Oz on a plane is OzPOy lies in the XOY plane and is perpendicular to OzPOx is determined by the right-hand rule;
the step (2) is to construct a cuboid box surrounding the outer surface of the spacecraft, and 6 surfaces of the cuboid are expressed as projection coordinate system
The surface of the spacecraft is dispersed by triangular units, N is the number of the triangular units on the surface of the spacecraft, (x)i,yi,zi),i∈[1,N]Coordinates of the triangular unit nodes in a projection coordinate system;
the boundary rectangle in the step (3) is perpendicular to the projection direction and is positioned at the upstream of the cuboid box, and the coordinates of the boundary rectangle meet the requirement
Initial coordinate r in step (4)0(x0,y0,z0) The method specifically comprises the following steps:
in the formula, R1、R2Random numbers which are uniformly distributed in the interval of (0, 1);
judging whether the motion trail of the test particle ray intersects with the triangular unit on the surface of the spacecraft in the step (5), and specifically comprising the following steps of:
(5.1) calculating the motion trail of the test particle ray: according to the initial position coordinates r of the test particles0(x0,y0,z0) And the projection direction to obtain a ray parameter equation of
Wherein t is a time parameter;
(5.2) calculating an equation of the plane where the triangular unit is located: let the coordinate of any vertex of triangle ABC be (x)1,y1,z1) The surface normal vector is n ═ n (n)1,n2,n3) Then the equation of the plane in which it is located is
n·(x-x1,y-y1,z-z1)＝0；
(5.3) judging whether the ray track of the test particle intersects with the plane of the triangular unit: simultaneous ray parameter equation and equation of triangle plane
If n is3If 0, the plane is parallel to the ray, the two do not intersect, otherwise, the result is obtained
If t is less than or equal to 0, the ray does not intersect with the plane and further does not intersect with the triangle unit, if t is greater than 0, the step (5.4) is carried out to further judge whether the intersection point is inside the triangle ABC;
(5.4) substituting the value of the parameter t into the ray parameter equation to obtain the coordinate (x) of the intersection point PP,yP,zP) Is composed of
Order to
If at the same time satisfy
If the intersection point P is inside the triangle ABC, the ray motion trail of the test particle is intersected with the triangle unit on the surface of the spacecraft, otherwise, the intersection point is outside the triangle ABC, and the ray motion trail is not intersected with the triangle unit;
the projected area A of the spacecraft is counted in the step (7)PThe concrete formula is
AP＝(xmax-xmin)(ymax-ymin)(Q/M)
Wherein M is the total number of the generated and tracked test particles, and Q is the number of the test particles of which the motion trail intersects with the surface of the spacecraft.
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