CN107944094A - A kind of definite method and system of complex appearance spacecraft projected area - Google Patents
A kind of definite method and system of complex appearance spacecraft projected area Download PDFInfo
- Publication number
- CN107944094A CN107944094A CN201711076808.8A CN201711076808A CN107944094A CN 107944094 A CN107944094 A CN 107944094A CN 201711076808 A CN201711076808 A CN 201711076808A CN 107944094 A CN107944094 A CN 107944094A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- mtr
- mtd
- spacecraft
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Aviation & Aerospace Engineering (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Medicines Containing Antibodies Or Antigens For Use As Internal Diagnostic Agents (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
A kind of definite method and system of complex appearance spacecraft projected area, use for reference the thought of Monte Carlo technologies in statistics, with reference to ray basic in computational geometry and triangle intersection theory, computational methods of all preferable complex appearance spacecraft of a kind of robustness and versatility along any direction projected area are developed.First, a cuboid box for surrounding spacecraft outer surface just is built, which has a surface perpendicular to projecting direction；Then, it is determined that producing the bounding rectangles of test particle, plane where bounding rectangles is located at the upstream for surrounding box perpendicular to projecting direction；Again, test particle is produced in bounding rectangles, and tracks its movement locus, judge whether track intersects with spacecraft surface, intersection population is incremented by 1 if intersecting；Finally, previous step process is repeated until test particle sum is sufficiently large, to ensure numerical convergence, the projected area of spacecraft is counted according to intersection population and the test particle sum produced.
Description
Technical field
The present invention relates to a kind of definite method and system of complex appearance spacecraft projected area, belong to flight vehicle aerodynamic spy
Property design and posture orbits controlling technical field.
Background technology
In recent years, due to the needs that gravitational field and stable state ocean circulation accurately measure, beyond low Earth orbit (200-500km)
Spacecraft gradually shows wide application prospect, however, realizing that the prerequisite that gravity gradient accurately measures is low orbit satellite
The accurate calculating of aerodynamic drag.Aerodynamic drag is mainly by the projection of local atmospheric density, resistance coefficient and satellite along the direction of motion
Area together decides on.Local atmospheric density is generally provided by Atmospheric models, and pneumatic drag coefficient can be with reference database, it is also necessary to
Solve the problems, such as to be exactly to calculate its projected area along the direction of motion.
Recently, solar sail detector shows huge potentiality in deep-space detection field, because it utilizes solar light pressure
Power obtains motive force, it is not necessary to carries a large amount of propellants.Although solar light pressure very little, constantly accelerate to reach detector
One considerable speed, may ultimately reach the speed of 5-10 times of conventional aerospace device.The attitude and orbit control of solar sail detector
System needs the input of solar pressure, and solar pressure is then with solar flux, solar sail surface reflectivity and along radiation direction
Projected area it is related.Solar flux is physical constant, and reflectivity is material properties, can be surveyed by consulting reference books or experiment
Amount obtains, and the calculating of solar pressure is just attributed to calculating of the solar sail along radiation direction projected area.
In addition, a ring important in spacecraft shield system design and risk assessment is micrometeroroid or space junk and boat
Its device components hit probability is estimated, with the proviso that providing spacecraft and its all parts in the given throwing threatened on direction of attack
Shadow area.Meanwhile the projected area of satellite along a direction is more directly the necessary input parameter of its gesture stability, such as the sun
Aiming at (Sun-pointing) gesture mode needs to input projected area of the satellite along sunray direction, minimum or maximum resistance
(minimum-drag or maximum-drag) gesture mode then needs to identify and calculate the minimum or maximal projection of satellite
Area.
Projection of the geometry entity along certain direction is generated, is known as blocking algorithm in field of Computer Graphics, is computational geometry
A kind of numerical method directly perceived of solid projection area, so far still among continuous research and improving.At present, computer graphics
Widely used projection algorithm is light projection and ray trace method：Light projection method calculates the light launched from light source
With the intersection point on geometry entity surface, visible face (non-visible face is shady face) is identified by minimum range, then using polygon
Shape projection algorithm projects visible face the projected image that can generate geometry entity；Ray trace method is in light projection side
On the basis of method, it is contemplated that light scatters and reflection effect.
However, the either calculating of low orbit satellite atmospheric drag, solar sail detector optical pressure, or spacecraft shield design
With risk assessment, and Spacecraft Attitude Control, the input of spacecraft (component) projected area is all only needed, passes through computer graphic
The method generation projected image of shape calculates projected area and obviously takes time and effort again.Foreign countries have researcher to be managed based on convex polygon
By having developed a kind of calculating analytic method of the spacecraft along any direction projected area.Since each process uses analytic solutions
Form realize that the computational efficiency of this method is very high.However, after the spacecraft progress polygon of complex appearance is discrete, it is thrown
Shadow polygon inevitably in the presence of even three or more than three polygons while intersecting situation is intersected two-by-two, causes calculating projection more
The area of side shape intersection is exceedingly difficult, even may not.Moreover, parsing characteristic cause its robustness and versatility compared with
Difference, under some extreme cases, the intrinsic rounding error of computer can cause the result of calculation of mistake.Spacecraft shape is more complicated,
The possibility for extreme case occur is bigger.Therefore, although above-mentioned analytic method is efficient, it is difficult to apply to aerospace engineering practice
In.
The content of the invention
The technology of the present invention solves the problems, such as：A kind of overcome the deficiencies in the prior art, it is proposed that complex appearance spacecraft edge
The definite method and system of any direction projected area, complex appearance spacecraft perspective plane can not be calculated in the prior art by solving
The problem of accumulating such as.
The present invention technical solution be：
A kind of definite method of complex appearance spacecraft projected area, comprises the following steps：
(1) projected coordinate system Oxyz is built；
(2) cuboid box for surrounding spacecraft outer surface is built, 3 orthogonal ribs of cuboid are put down respectively
Row is in x, y and z axes；
(3) bounding rectangles of generation test particle are determined；
(4) test particle is randomly generated in the bounding rectangles that step (3) provides, provides test particle in projected coordinate system
Middle initial coordinate r0；
(5) judge whether test particle ray movement locus intersects with spacecraft surface triangles unit：If without phase
Hand over, pass directly to step (6)；If intersecting, make intersection population Q be incremented by 1, then proceed to perform step (6)；
(6) whether the test particle sum M for judging to produce is less than preset value, if less than preset value, goes to step (4),
Otherwise step (7) is continued to execute；
(7) according to the intersection population Q and the test particle sum M produced, the projected area of spacecraft is counted.
Projected coordinate system Oxyz is built, is specially：
(1.1) body coordinate system OXYZ is built first, and coordinate origin is spacecraft centroid O, X, Y and Z axis and spacecraft
The principal axis of inertia overlaps；
(1.2) according to body coordinate system OXYZ, projected coordinate system Oxyz is built, projected coordinate system origin is located at spacecraft matter
Heart O, z-axis positive direction are projecting direction, make Oz be projected as Oz in planeP, then Oy be located in XOY plane and perpendicular to OzP, Ox
Determined by the right-hand rule.
The step (2) builds a cuboid box for surrounding spacecraft outer surface, and 6 faces of the cuboid are projecting
Coordinate system is expressed as
Spacecraft surface is discrete by triangular element, and N is spacecraft surface triangles element number, (xi,yi,zi),i∈
[1, N] it is coordinate of the triangular element node in projected coordinate system.
Step (3) bounding rectangles are expired perpendicular to projecting direction, and positioned at the upstream of the cuboid box, its coordinate
Foot
Initial coordinate r in step (4)0(x0,y0,z0) be specially：
In formula, R1、R2It is the equally distributed random number in (0,1) section.
Judge whether test particle ray movement locus intersects with spacecraft surface triangles unit in the step (5),
Specifically include following steps：
(5.1) test particle ray movement locus is calculated：According to test particle initial position co-ordinates r0(x0,y0,z0) and throw
Shadow direction, obtaining ray parameter equation is
Wherein, t is time parameter；
(5.2) equation of plane where calculating triangular element：The coordinate for making any one vertex of triangle ABC is (x1,
y1,z1), normal vector is n=(n outside surface1,n2,n3), then the equation of plane where it is
n·(x-x1,y-y1,z-z1)=0；
(5.3) judge whether test particle ray tracing intersects with plane where triangular element：Simultaneous ray parameter side
The equation of plane where journey and triangle
If n3=0, then for plane parallel to ray, both are non-intersect, otherwise try to achieve
If t≤0, ray is non-intersect with plane, into without intersecting with triangular element, if t ＞ 0, enter
Whether step (5.4) determines whether intersection point inside triangle ABC；
(5.4) value of parameter t is substituted into ray parameter equation, obtains the coordinate (x of intersection point PP,yP,zP) be
Order
If meet at the same time
Then intersection point P is inside triangle ABC, test particle ray movement locus and spacecraft surface triangles unit phase
Hand over, otherwise for intersection point outside triangle ABC, ray movement locus and triangular element are non-intersect.
Preset value in the step (6) is more than or equal to 106。
The projected area A of statistics spacecraft in the step (7)P, specific formula is
AP=(xmax-xmin)(ymax-ymin)(Q/M)
In formula, M is the test particle sum for producing and tracking, and Q is the experiment grain that movement locus intersects with spacecraft surface
Subnumber.
The value range 10 of the preset value6~108。
A kind of definite system of complex appearance spacecraft projected area, including：
Coordinate system builds module：For building projected coordinate system Oxyz；
Box builds module：For building a cuboid box for surrounding spacecraft outer surface, 3 ribs point of cuboid
Not parallel to x, y and z axes；
Bounding rectangles generation module：For determining the bounding rectangles of generation test particle；
Test particle generation module：For randomly generating experiment grain in the bounding rectangles that bounding rectangles generation module determines
Son, provides test particle initial coordinate r in projected coordinate system0；
Intersecting judgment module：For judge test particle ray movement locus whether with spacecraft surface triangles unit phase
Hand over, and count intersection population Q；
Projected area computing module：For according to the intersection population Q that intersecting judgment module counts and generation
Test particle sum M, counts the projected area of spacecraft.
The present invention compared with prior art the advantages of：
(1) computational methods of current complex appearance spacecraft projected area, otherwise given birth to by the method for computer graphics
Calculate projected area again into projected image and seem and take time and effort, otherwise cause to lead to based on the theoretical method using parsing of convex polygon
It is poor with property and robustness and aerospace engineering can not be applied to.Based on this, the present invention uses for reference Monte Carlo technologies in statistics
Thought, with reference to ray basic in computational geometry and triangle intersection theory, developed a kind of complex appearance spacecraft edge
The computational methods of any direction projected area.
(2) relative to the projection algorithm of computer graphics, the method for the present invention calculating speed is fast, and memory requirement is low, relatively
For the analytic method based on convex polygon theory, the method for the present invention robustness and versatility are good, and it is arbitrarily complicated to possess processing
The ability of engineering shape.In addition, the method for the present invention calculates the time with the increasing of calculation scale, problem complexity and space dimensionality
It is big in a linear relationship, it is the ideal method that complex appearance spacecraft projected area calculates.
Brief description of the drawings：
Fig. 1：The method of the present invention flow chart；
Fig. 2：Body coordinate system and projected coordinate system schematic diagram；
Fig. 3：Single side circle tablet schematic diagram (a) and its triangular element discretization (b)；
Fig. 4：Single side circle tablet result of calculation and notional result comparison diagram；
Fig. 5：SAMSON dummy satellite schematic diagrames；
Fig. 6：SAMSON satellites projected area with the change of its posture, wherein, Fig. 6 (a) is three-dimensional distribution map, Fig. 6 (b)
For equivalent curve；
Fig. 7：GOCE dummy satellite schematic diagrames, wherein Fig. 7 (a) are cephalad direction view, and Fig. 7 (b) is caudal directions view；
Fig. 8：GOCE satellites projected area is with the change of its posture；Wherein, Fig. 8 (a) is three-dimensional distribution map, and Fig. 8 (b) is
Equivalent curve.
Embodiment
The needs calculated according to existing complex appearance spacecraft projected area, use for reference Monte Carlo technologies in statistics
Thought, with reference to ray basic in computational geometry and triangle intersection theory, the present invention proposes a kind of complex appearance boat
Computational methods of its device along any direction projected area.
First, a cuboid box for surrounding spacecraft outer surface just is built, which has the surface vertical
In projecting direction；Then, it is determined that produce the bounding rectangles of test particle, plane where bounding rectangles perpendicular to projecting direction, and
Positioned at the upstream for surrounding box；Again, test particle is produced in bounding rectangles, provides its position coordinates, and track the experiment grain
The movement locus of son, judges whether track intersects with spacecraft surface triangles unit, makes intersection population if intersecting
It is incremented by 1, otherwise carries out in next step；Finally, previous step process is repeated until test particle sum is sufficiently large, to ensure result of calculation
Convergence, the projected area of spacecraft is counted according to intersection population and the test particle sum produced.
As shown in Figure 1, concretely comprise the following steps：
(1) body coordinate system B and projected coordinate system P is built, the specific implementation process is as follows：
The coordinate origin of body coordinate system B is located at spacecraft centroid O, X, Y and Z axis is overlapped with the spacecraft principal axis of inertia.Throw
The origin of shadow coordinate system P is similarly positioned in spacecraft centroid O, its z-axis is overlapped with projecting direction, i.e., projecting direction is Oz axis, makes Oz
Oz is projected as in planeP, then Oy be located in XOY plane and perpendicular to OzP, Ox determined by the right-hand rule,
As shown in Figure 2.Using space structure mechanics or astronomical term, the inclination angle of Oz and XOY plane is defined as red
Latitude δ, in the range of δ ∈ [- pi/2, pi/2], OzPBe defined as right ascension α with the angle of OX, in the range of α ∈ [0,2 π).It is if no special
Illustrate, coordinate or vector hereinafter are the amount in projected coordinate system P.
(2) cuboid box for surrounding spacecraft outer surface just, 3 orthogonal ribs point of cuboid are built
Not parallel to the x, y and z axes of projected coordinate system.In general, complex appearance spacecraft surface is discrete by triangular element, if surface three
Corner shaped elements quantity is N, and coordinate of the cell node in projected coordinate system is (xi,yi,zi), i ∈ [1, N], then the cuboid box
6 faces of son are determined by following formula
(3) bounding rectangles of generation test particle are determined.Plane where bounding rectangles is located at bag perpendicular to projecting direction
The upstream of box is enclosed, its coordinate meets
(4) bounding rectangles provided in step (3) randomly generate test particle, provide test particle in projected coordinate system
Position, initial coordinate r0(x0,y0,z0) be
R1、R2It is the equally distributed random number in (0,1) section.
(5) judge whether test particle ray movement locus intersects with spacecraft surface triangles unit：If without phase
Hand over, pass directly to step (6)；If intersecting, make intersection population Q be incremented by 1, then proceed to perform step (6).Q's
Initial value is 0；The specific implementation process is as follows：
(5.1) test particle ray movement locus is calculated.According to test particle initial position co-ordinates r0(x0,y0,z0) and throw
Shadow direction, it is easy that its parametric equation is
(5.2) equation of plane where calculating triangular element.The coordinate for making any one vertex of triangle ABC is (x1,
y1,z1), normal vector is n=(n outside surface1,n2,n3), then the equation of plane where it is
n·(x-x1,y-y1,z-z1)=0
(5.3) judge whether test particle ray tracing intersects with plane where triangular element.Simultaneous ray parameter side
The equation of plane where journey and triangle
If n3=0, then for plane parallel to ray, both are obviously non-intersect, otherwise easily try to achieve
If t≤0, ray is non-intersect with plane, will not intersect naturally with triangular element, otherwise needs to determine whether
Whether intersection point is inside triangle ABC.
(5.4) if test particle ray movement locus intersects, it is necessary to whether judge intersection point P with plane where triangle ABC
Inside triangle ABC.The value for substituting into parameter t arrives ray parameter equation, the easy coordinate (x for obtaining intersection point PP,yP,zP) be
Order
If meet at the same time
Then intersection point P is inside triangle ABC, test particle ray movement locus and spacecraft surface triangles unit phase
Hand over, otherwise for intersection point outside triangle ABC, ray movement locus and triangular element are non-intersect.
(6) whether the test particle sum for judging to produce and track is less than preset value, if less than preset value, goes to step
(4), step (7) is otherwise continued to execute.
The quantity of the test particle generally tracked is more than or equal to 106When, start to count projected area.According to statistical error and
Time information summary is calculated to consider, can be 106~108Interior value.
(7) projected area of spacecraft is counted.If the test particle number for producing and tracking is M, wherein, movement locus and boat
The test particle number that its device surface is intersected is Q, then projected area A of the spacecraft along z-axisPFor
AP=(xmax-xmin)(ymax-ymin)(Q/M)
Statistical error ε is single error distribution standard deviation σ and the subduplicate business of test particle sum, i.e.,
So after producing and tracking enough test particles, projected area is bound to restrain, and statistical error is
The specific solution example that complex appearance spacecraft projected area calculates is as follows：
Consider first shape is simple, projected area there are analytic solutions single side circle tablet, easy to comparative analysis.It is single
Face circle tablet schematic diagram, body coordinate system and projecting direction are as shown in Figure 3a, axial, open up to being respectively X, Y and Z with normal direction
Axis, axis of projection are z-axis.Circular tablet radius is 1m, due to axial symmetry characteristic, it is only necessary to considers the situation of right ascension α=0 °.Cause
This, z-axis is located at XOZ planes, and the angle with X-axis is declination δ, and the angle with Z axis is the complementary angle of declination.Using 608 triangles
Unit progress is discrete, and as shown in Figure 3b, test particle sum is 2 × 107, at this time statistical error be
Fig. 4 gives change of the single side flat projection area with declination, and the excursion of declination is δ ∈ [0 °, 90 °],
I.e. projecting direction is changed to perpendicular to planar surface from parallel to planar surface.When projecting direction is parallel to planar surface (δ=
90 °), projected area 0；When projecting direction is perpendicular to planar surface (δ=90 °), projected area is platen area π；With throwing
From when changing to parallel to planar surface perpendicular to planar surface, projected area increases in SIN function in shadow direction.
For the simple shape, the Theory Solution of projected area is the product of platen area and declination sine, i.e.,
AP=π cos (pi/2-δ)=π sin δ
Obviously, Monte Carlo statistical results of the present invention are completely the same with Theory Solution, demonstrate the reliability of method.
Then, the SAMSON moonlets of European Space Agency are considered, as shown in Figure 5.Table 1 lists SAMSON satellites along several
The projected area of typical directions (declination δ and right ascension α), give result of calculation of the present invention, reliable result by references and both
Relative error.During declination δ=90 °, projecting direction is overlapped with the Z axis of body coordinate system, therefore projected area is unrelated with right ascension.Experiment
Total number of particles is 2 × 107, corresponding statistical error isMeet engineering demand.It can see from table, the present invention
Result of calculation is consistent with the data of document report, and the magnitude of relative error isIt is identical with statistical error magnitude.Cause
This, Monte Carlo technologies proposed by the present invention are suitable for complex engineering application shape, possess accurate calculating complex appearance space flight
Ability of the device along any direction projected area, and relative error meets Statistical Distribution.
Fig. 6 is projected area of the SAMSON satellites along different directions, and Fig. 6 (a) is projected area three-dimensional distribution map, Fig. 6 (b)
For corresponding two dimensional equivalent line chart, the excursion of declination is δ ∈ [- 90 °, 90 °], the excursion of right ascension for α ∈ [0 °,
360°].During declination δ=- 90 °, projecting direction is Z axis opposite direction；During declination δ=0 °, projecting direction is parallel to XOY plane；It is red
During latitude δ=90 °, projecting direction is Z axis positive direction.Obviously, SAMSON satellites along different directions projected area excursion across
Spend it is larger, from minimum value APmin=0.03m2Change to maximum APmax=0.194m2.In addition, when solar sail is unfolded, declination,
That is the angle of projecting direction and XOY plane, the influence to projected area become apparent.In contrast, the influence smaller one of right ascension
A bit, this is that the geometric shape of SAMSON satellites is determined.Near declination δ=0 °, projected area is minimum, and right ascension is to throwing at this time
The influence of shadow area is maximum；During declination δ=± 90 °, projected area is maximum, and right ascension does not influence projected area at this time.Fig. 6 takes off
The relation of the attitude of satellite and its projected area is shown, has been the necessary input condition of satellite gravity anomaly.
Projected area under 1 SAMSON satellite typical case's postures of table
Finally, as projected area Monte Carlo simulations method in the application of aerospace engineering, European Space Agency is considered
Gravitational field and stable state ocean circulation explorer satellite (Gravity field and steady state Ocean Circulation
Explorer, GOCE), as shown in Fig. 7 (a), 7 (b).
Fig. 8 is projected area of the GOCE satellites along different directions, and Fig. 8 (a) is projected area three-dimensional distribution map, and Fig. 8 (b) is
Corresponding two dimensional equivalent line chart, the excursion of declination are δ ∈ [- 90 °, 90 °], the excursion of right ascension for α ∈ [0 °,
360°].Similar with SAMON satellites, near declination δ=0 °, GOCE projected areas are minimum, at this time shadow of the right ascension to projected area
Ring maximum；During declination δ=± 90 °, projected area is maximum, and right ascension does not influence projected area at this time.However, GOCE satellites are thin
The shape of long body, the larger area of additional solar wing, cause its along different directions projected area span than SAMSON satellite more
Greatly, from minimum value APmin=0.817m2Change to maximum APmax=10.273m2.With the change of its posture, GOCE satellites are thrown
The so big excursion of shadow area causes its suffered atmospheric drag and solar light pressure change huge, while can also cause the sun
The acute variation of wing generating efficiency, proposes its stability, attitude and orbit control huge challenge.Fig. 8 discloses GOCE
The relation of the attitude of satellite and its projected area, is that solar wing generated energy is calculated with monitoring, atmospheric drag and solar light pressure are predicted
Input parameter, and the attitude of satellite and the necessary condition of orbits controlling.
In summary the calculating of single side circle flat plate model, SAMSON satellites and GOCE satellite projected areas can obtain with
Draw a conclusion：Spacecraft projected area computational methods of the present invention, which possess, accurately to be calculated arbitrarily complicated spacecraft shape and is thrown along any direction
The ability of shadow area, robustness and versatility are good, can provide the relation of the attitude of satellite and its projected area, are complex appearance boats
The ideal method that its device projected area calculates.
The undisclosed technology of the present invention belongs to general knowledge well known to those skilled in the art.
Claims (10)
- A kind of 1. definite method of complex appearance spacecraft projected area, it is characterised in that comprise the following steps：(1) projected coordinate system Oxyz is built；(2) cuboid box for surrounding spacecraft outer surface is built, 3 orthogonal ribs of cuboid are respectively parallel to X, y and z axes；(3) bounding rectangles of generation test particle are determined；(4) test particle is randomly generated in the bounding rectangles that step (3) provides, it is first in projected coordinate system provides test particle Beginning coordinate r0；(5) judge whether test particle ray movement locus intersects with spacecraft surface triangles unit：If do not intersected, directly It is switched to step (6)；If intersecting, make intersection population Q be incremented by 1, then proceed to perform step (6)；(6) whether the test particle sum M for judging to produce is less than preset value, if less than preset value, goes to step (4), otherwise Continue to execute step (7)；(7) according to the intersection population Q and the test particle sum M produced, the projected area of spacecraft is counted.
- A kind of 2. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：Structure Projected coordinate system Oxyz, is specially：(1.1) body coordinate system OXYZ is built first, and coordinate origin is spacecraft centroid O, X, Y and Z axis and spacecraft inertia Main shaft overlaps；(1.2) according to body coordinate system OXYZ, projected coordinate system Oxyz is built, projected coordinate system origin is located at spacecraft centroid O, Z-axis positive direction is projecting direction, makes Oz be projected as Oz in planeP, then Oy be located in XOY plane and perpendicular to OzP, Ox passes through The right-hand rule determines.
- A kind of 3. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：It is described Step (2) builds a cuboid box for surrounding spacecraft outer surface, and 6 faces of the cuboid are expressed as in projected coordinate system<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>min</mi> </msub> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <munder> <mi>max</mi> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>min</mi> </msub> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <munder> <mi>max</mi> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>min</mi> </msub> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <munder> <mi>max</mi> <mrow> <mi>i</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>&rsqb;</mo> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>Spacecraft surface is discrete by triangular element, and N is spacecraft surface triangles element number, (xi,yi,zi),i∈[1,N] For coordinate of the triangular element node in projected coordinate system.
- A kind of 4. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：It is described Step (3) bounding rectangles meet perpendicular to projecting direction, and positioned at the upstream of the cuboid box, its coordinate<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
- A kind of 5. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：Step (4) initial coordinate r in0(x0,y0,z0) be specially：<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>z</mi> <mi>min</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>In formula, R1、R2It is the equally distributed random number in (0,1) section.
- A kind of 6. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：It is described Judge whether test particle ray movement locus intersects with spacecraft surface triangles unit in step (5), specifically include following Step：(5.1) test particle ray movement locus is calculated：According to test particle initial position co-ordinates r0(x0,y0,z0) and projection side To obtaining ray parameter equation is<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>t</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>t</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mrow>Wherein, t is time parameter；(5.2) equation of plane where calculating triangular element：The coordinate for making any one vertex of triangle ABC is (x1,y1, z1), normal vector is n=(n outside surface1,n2,n3), then the equation of plane where it is n (x-x1,y-y1,z-z1)=0；(5.3) judge whether test particle ray tracing intersects with plane where triangular element：Simultaneous ray parameter equation and The equation of plane where triangle<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>+</mo> <mi>t</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>n</mi> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced>If n3=0, then for plane parallel to ray, both are non-intersect, otherwise try to achieve<mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>n</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <msub> <mi>n</mi> <mn>3</mn> </msub> </mfrac> <mo>+</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>,</mo> </mrow>If t≤0, ray is non-intersect with plane, into without intersecting with triangular element, if t ＞ 0, enters step (5.4) Determine whether intersection point whether inside triangle ABC；(5.4) value of parameter t is substituted into ray parameter equation, obtains the coordinate (x of intersection point PP,yP,zP) be<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>P</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>P</mi> </msub> <mo>=</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>P</mi> </msub> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>/</mo> <msub> <mi>n</mi> <mn>3</mn> </msub> <mo>+</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>Order<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>A</mi> <mi>P</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>,</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>A</mi> <mi>B</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mo>&RightArrow;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>3</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>B</mi> <mi>P</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>,</mo> <msub> <mi>p</mi> <mn>4</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>B</mi> <mi>A</mi> </mrow> <mo>&RightArrow;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>5</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>C</mi> <mi>A</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>C</mi> <mi>P</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>,</mo> <msub> <mi>p</mi> <mn>6</mn> </msub> <mo>=</mo> <mover> <mrow> <mi>C</mi> <mi>A</mi> </mrow> <mo>&RightArrow;</mo> </mover> <mo>&times;</mo> <mover> <mrow> <mi>C</mi> <mi>B</mi> </mrow> <mo>&RightArrow;</mo> </mover> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>If meet at the same time<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>&CenterDot;</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>></mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>3</mn> </msub> <mo>&CenterDot;</mo> <msub> <mi>p</mi> <mn>4</mn> </msub> <mo>></mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mn>5</mn> </msub> <mo>&CenterDot;</mo> <msub> <mi>p</mi> <mn>6</mn> </msub> <mo>></mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>Then inside triangle ABC, test particle ray movement locus intersects intersection point P with spacecraft surface triangles unit, no Then for intersection point outside triangle ABC, ray movement locus and triangular element are non-intersect.
- A kind of 7. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：It is described Preset value in step (6) is more than or equal to 106。
- A kind of 8. definite method of complex appearance spacecraft projected area according to claim 1, it is characterised in that：It is described The projected area A of statistics spacecraft in step (7)P, specific formula isAP=(xmax-xmin)(ymax-ymin)(Q/M)In formula, M is the test particle sum for producing and tracking, and Q is the test particle number that movement locus intersects with spacecraft surface.
- A kind of 9. definite method of complex appearance spacecraft projected area according to right wants 7, it is characterised in that：It is described pre- If the value range 10 of value6~108。
- A kind of 10. definite system of complex appearance spacecraft projected area, it is characterised in that including：Coordinate system builds module：For building projected coordinate system Oxyz；Box builds module：For building a cuboid box for surrounding spacecraft outer surface, 3 ribs of cuboid are put down respectively Row is in x, y and z axes；Bounding rectangles generation module：For determining the bounding rectangles of generation test particle；Test particle generation module：For randomly generating test particle in the bounding rectangles that bounding rectangles generation module determines, Provide test particle initial coordinate r in projected coordinate system0；Intersecting judgment module：For judging whether test particle ray movement locus intersects with spacecraft surface triangles unit, And count intersection population Q；Projected area computing module：For the intersection population Q counted according to intersecting judgment module and the experiment produced Total number of particles M, counts the projected area of spacecraft.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711076808.8A CN107944094B (en) | 2017-11-06 | 2017-11-06 | Method and system for determining projection area of spacecraft with complex appearance |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711076808.8A CN107944094B (en) | 2017-11-06 | 2017-11-06 | Method and system for determining projection area of spacecraft with complex appearance |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107944094A true CN107944094A (en) | 2018-04-20 |
| CN107944094B CN107944094B (en) | 2021-04-13 |
Family
ID=61933357
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711076808.8A Active CN107944094B (en) | 2017-11-06 | 2017-11-06 | Method and system for determining projection area of spacecraft with complex appearance |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107944094B (en) |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112182757A (en) * | 2020-09-27 | 2021-01-05 | 北京空间飞行器总体设计部 | Spacecraft vulnerability assessment method under space debris and micro-fluidic star environment |
| CN113139995A (en) * | 2021-04-19 | 2021-07-20 | 杭州伯资企业管理合伙企业(有限合伙) | Low-cost method for detecting and evaluating light occlusion between objects |
| CN113158341A (en) * | 2021-04-19 | 2021-07-23 | 北京航天飞行控制中心 | Spacecraft relay terminal antenna tracking forecasting method, device and storage medium |
| CN114880943A (en) * | 2022-05-24 | 2022-08-09 | 安及义实业（上海）有限公司 | Bioreactor design method and system based on database |
| CN116304484A (en) * | 2023-01-10 | 2023-06-23 | 广东科学技术职业学院 | High-precision estimation method and system for grid model vertex normal vector |
| CN117372502A (en) * | 2023-11-15 | 2024-01-09 | 北京理工大学 | Group target projection area calculation method and system for target vulnerability analysis |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5557106A (en) * | 1995-08-15 | 1996-09-17 | Alarm Device Manufacturing Co. | Rodent discriminator lens |
| CN102053258A (en) * | 2010-12-15 | 2011-05-11 | 中国石油集团川庆钻探工程有限公司 | Self-adaptive three-dimensional ray tracing method based on complex geological structure |
| CN102346922A (en) * | 2010-07-30 | 2012-02-08 | 中国科学院遥感应用研究所 | Space remote sensing load imaging geometric distortion three-dimensional visualization simulation method |
-
2017
- 2017-11-06 CN CN201711076808.8A patent/CN107944094B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5557106A (en) * | 1995-08-15 | 1996-09-17 | Alarm Device Manufacturing Co. | Rodent discriminator lens |
| CN102346922A (en) * | 2010-07-30 | 2012-02-08 | 中国科学院遥感应用研究所 | Space remote sensing load imaging geometric distortion three-dimensional visualization simulation method |
| CN102053258A (en) * | 2010-12-15 | 2011-05-11 | 中国石油集团川庆钻探工程有限公司 | Self-adaptive three-dimensional ray tracing method based on complex geological structure |
Non-Patent Citations (2)
| Title |
|---|
| CHAMINDA KARUNASENA等: "Vision Based Cross Sectional Area Estimator for Industrial Rubber Profile Extrusion Process Controlling", 《IEEE XPLORE》 * |
| 靳旭红等: "超低轨航天器气动特性快速预测的试验粒子Monte Carlo方法", 《航空学报》 * |
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112182757A (en) * | 2020-09-27 | 2021-01-05 | 北京空间飞行器总体设计部 | Spacecraft vulnerability assessment method under space debris and micro-fluidic star environment |
| CN113139995A (en) * | 2021-04-19 | 2021-07-20 | 杭州伯资企业管理合伙企业(有限合伙) | Low-cost method for detecting and evaluating light occlusion between objects |
| CN113158341A (en) * | 2021-04-19 | 2021-07-23 | 北京航天飞行控制中心 | Spacecraft relay terminal antenna tracking forecasting method, device and storage medium |
| CN113139995B (en) * | 2021-04-19 | 2022-06-21 | 杭州伯资企业管理合伙企业(有限合伙) | Low-cost method for detecting and evaluating light occlusion between objects |
| CN114880943A (en) * | 2022-05-24 | 2022-08-09 | 安及义实业（上海）有限公司 | Bioreactor design method and system based on database |
| CN114880943B (en) * | 2022-05-24 | 2023-02-03 | 安及义实业（上海）有限公司 | Bioreactor design method and system based on database |
| CN116304484A (en) * | 2023-01-10 | 2023-06-23 | 广东科学技术职业学院 | High-precision estimation method and system for grid model vertex normal vector |
| CN116304484B (en) * | 2023-01-10 | 2023-11-17 | 广东科学技术职业学院 | High-precision estimation method and system for grid model vertex normal vector |
| CN117372502A (en) * | 2023-11-15 | 2024-01-09 | 北京理工大学 | Group target projection area calculation method and system for target vulnerability analysis |
| CN117372502B (en) * | 2023-11-15 | 2024-05-14 | 北京理工大学 | Group target projection area calculation method and system for target vulnerability analysis |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107944094B (en) | 2021-04-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107944094A (en) | A kind of definite method and system of complex appearance spacecraft projected area | |
| US8805655B2 (en) | Numerical method for simulating subsonic flows based on euler equations in lagrangian formulation | |
| Wang | Adaptive high-order methods in computational fluid dynamics | |
| Sambasivan et al. | Ghost fluid method for strong shock interactions part 1: Fluid-fluid interfaces | |
| Gao et al. | Particle simulations of planetary probe flows employing automated mesh refinement | |
| Morton et al. | DES grid resolution issues for vortical flows on a delta wing and an F-18C | |
| CN103268067B (en) | A kind of satellite based on intending hypercomplex number and plan hypercomplex number kinematical equation points to tracking and controlling method | |
| Williams et al. | QUIC-PLUME theory guide | |
| Xie et al. | Robust and efficient prediction of the collection efficiency in icing accretion simulation for 3D complex geometries using the Lagrangian approach I: an adaptive interpolation method based on the restricted radial basis functions | |
| CN111310381A (en) | Three-dimensional water drop collection coefficient calculation method | |
| CN111008481A (en) | Pneumatic analysis method and device for spacecraft | |
| CN103593551A (en) | Sunlight pressure computing method based on high-orbit optical imaging satellite | |
| CN114012726A (en) | Aerospace mechanical arm collision detection method | |
| Sequeira et al. | Comparing aerodynamic models for numerical simulation of dynamics and control of aircraft | |
| CN104392030A (en) | Curved surface machining method based on STL (Standard Template Library) three-dimensional model | |
| Papadakis et al. | Simulation of ice shedding from a business jet aircraft | |
| Ignatowicz et al. | Dynamic moment model for numerical simulation of a 6-DOF plate trajectory around an aircraft | |
| CN105183948B (en) | A kind of high-precision satellite sun solar radiation perturbation force modeling method based on secondary reflection | |
| Murman et al. | Cartesian-grid simulations of a canard-controlled missile with a spinning tail | |
| Meakin | Multiple-body proximate-flight simulation methods | |
| CN108734181B (en) | A method of accelerating online generation nuclear reactor characteristic curve | |
| Strömberg et al. | Tove time invariant Tti, exemplified with images from lateral light, entries of SO (3), quantum mechanics, touchscreens, photovoltaic and whirl formations | |
| Eriksson et al. | Grid generation and inviscid flow computation about a cranked-wingedairplane geometry | |
| Lukáčová-Medviďová et al. | Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics | |
| Cai et al. | Further investigation of the six-DOF hollow gravity anchor: Impact of the internal slant angle |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |