CN116495196A - Determination method for deep space exploration spacecraft star capturing orbit - Google Patents
Determination method for deep space exploration spacecraft star capturing orbit Download PDFInfo
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Abstract
The invention discloses a method for determining a stars capturing orbit of a deep space exploration spacecraft, which is suitable for orbit design and optimization of a stars capturing task; the novel capturing strategy is provided, and simultaneously, the capturing orbit is changed by utilizing the attraction of the natural satellite of the wooden star and the sun so as to meet different requirements in the capturing process, and a design scheme with higher precision can be provided for the given expected near-wooden point radius; when the wooden star capturing orbit is designed, compared with the traditional capturing scheme, the wooden star capturing orbit has obvious speed increment saving and partially meets the requirements of subsequent detection tasks.
Description
Technical Field
The invention belongs to the technical field of aerospace, and particularly relates to a method for determining a stars capturing orbit of a deep space exploration spacecraft.
Background
In an extraterrestrial planetary exploration mission, capturing the incoming planetary gravitational field from the interplanetary space is one of the important links of the mission. For the detection of the wooden star, because a plurality of natural satellites exist in the wooden star and the action of multi-celestial body gravitation including sun and wooden star gravitation exists, if the orbit is designed and captured by adopting a classical conic curve splicing method only in the initial orbit design stage, larger errors exist between the orbit and a high-precision model, the natural satellites of the wooden star are not fully utilized for auxiliary capture, and finally the orbit is not changed by utilizing the perturbation of the sun gravitation, so that the orbit is captured by the wooden star with reasonable design and low energy, which is necessary for completing the capture of the spacecraft. In addition, the design of the capturing orbit needs to consider reducing the radiation of the wooden star and the orbit requirement of the subsequent detection task, so that an orbit determination method is required to be provided at present so as to reduce the speed increment required by capturing by utilizing other celestial attraction and meet the radius requirement of the subsequent detection orbit.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for determining the wooden star capturing orbit of a deep space exploration spacecraft, which aims to solve the problems that in the prior art, more speed increment is needed for direct capturing, the near wooden point is lower due to the assistance of wooden guard attraction, and more speed increment is needed for changing the semi-diameter of the near wooden point to meet the requirement of the orbit of a subsequent exploration task. In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for determining a spacecraft star capturing orbit comprises the following steps:
step S1: selecting an optimization variable, and determining a period of the track expected to be captured and a radius of a near wood point of the track expected to be captured;
step S2: determining calculation parameters of a wood guard attraction auxiliary process under the zero influence ball model;
step S3: according to the optimization variable and the wooden sanitation attraction auxiliary process calculation parameter, a two-body problem analysis formula is utilized to reversely push the wooden sanitation flying from a near wooden point to a wooden sanitation flying position in time, and wooden sanitation flying calculation is completed to obtain wooden sanitation flying front and rear parameters;
step S4: finishing the splicing of track segments before and after flying based on the calculated parameters before and after flying the wooden sanitation, continuing to push the wooden sanitation to the next flying place, and repeating the steps S3 and S4 or the step S4;
step S5: determining the position of the spacecraft at the near wood point and the speed and maneuvering speed increment of the spacecraft after first maneuvering based on the optimized variable;
step S6: the method comprises the steps of utilizing a circular limiting three-body dynamics model to recursively and backward in time from a near wood point, so as to determine the far wood point state of the spacecraft;
step S7: based on the remote wood point state of the spacecraft and the optimization variable, updating the remote wood point speed of the spacecraft after the second maneuver, and utilizing a circular limiting three-body dynamics model to recursively push the remote wood point state to the near wood point from the new remote wood point state in time, so as to determine the next near wood point state of the spacecraft;
step S8: according to the expected post-capture orbit period, and based on the next near-wood point state of the spacecraft, calculating by using a two-body problem model to obtain a third maneuvering speed increment;
step S9: and according to the speed increment required by the three maneuvers, comparing the relation between the radius of the next near-wood point and the radius of the expected near-wood point, and selecting the corresponding capturing track under the condition of the least consumption speed increment.
As a preferred embodiment, the step S1 includes:
in the design of the capturing orbit, at least one auxiliary fly-over of wood Wei Yinli is contained in a section of hyperbolic orbit from a wood star influence ball to a near wood point, wherein the wood Wei Gongzhuai orbit is simplified into an ephemeris-free circular coplanar orbit, and the orbit calculation is simplified by utilizing a two-body problem analysis formula;
the orbit after the near wood point is calculated by introducing solar attraction by using a circular restriction three-dimensional dynamics model, wherein the circular restriction three-dimensional dynamics model performs dimensionless on various units, M and M respectively represent the solar mass and the wood star mass, M+m is recorded as mass units, the average distance between the sun and the wood star is unit length, the inverse of the angular velocity of the orbit of the sun and the wood star is unit time,the mass ratio is as follows;
selecting the diameter of the near wood pointPhase angle j, initial eccentricity +.>Residual speed at near wood point->And (d)Second-order motor value->As an optimization variable.
As a preferred embodiment, the step S2 includes:
determining the orbit radius of the satellite to be flown over around the orbit；
Determining the residual speed of a hyperbolic orbit of a spacecraft around a starNear wood point radius->；
Determining fly-by altitude。
As a preferable embodiment, the step S3 includes:
first according to a given near wood point diameterAnd the residual speed at the near wood point +.>Calculating a hyperbolic track semi-long axis by the formula (1):
（1）
the eccentricity e can then be obtained directly and the near wood point velocity v calculated using the given residual velocity p ：
（2）
（3）
In the method, in the process of the invention,is the constant of the attraction of the wooden star>=1.267127648/>10 8 ；
According to the diameter of the near wood pointAnd near wood point velocity v p The orbital angular momentum module value can be obtained:
（4）
after obtaining the angular momentum module value, according to the orbital equation, passing through the true near point angleTrack push was performed from 0 decrease:
（5）
when the orbit radius is the same as the orbit radius of the satellite to be flown, the satellite is regarded as carrying out a gravity assisted flying, and the satellite is firstly flown according to the orbit radius v m Calculating to obtain the satellite speed:
（6）
the near wood point diameter is reduced by the method (3)Changing to satellite orbit radius r m Residual speed at near wood point->Changing to the current track remaining speed +.>The spacecraft can be obtained at r=r m Velocity v at + I.e., the speed after the fly-by in the forward direction; obtaining the hyperbolic orbit residual speed of the spacecraft flying around the wooden guard by using the cosine law:
（7）
in the method, in the process of the invention,for the flying path angle after forward flying, the calculation formula is as follows:
（8）
wherein a and e are the semi-long axis and the eccentricity of the hyperbolic orbit around the star respectively; the steering angle of the hyperbola of the spacecraft winding Wei Feiyue, namely the included angle between the arrival residual speed and the departure residual speed is calculated by the residual speed and the flying height:
（9）
wherein R is m In order to fly over the radius of the satellite,is the gravitational parameter of the flying satellite; leaving the angle between the remaining speed and the satellite speed +.>The method is obtained by cosine theorem calculation:
（10）
angle between the remaining arrival speed and the satellite speedDetermined by the piecewise function:
（11）
the speed before forward fly-over and the flight path angle are obtained by the cosine law:
（12）。
as a preferable embodiment, the step S4 includes:
determining the radial velocity v of a spacecraft before flying over a wooden guard r And tangential velocity：
（13）
Using another representation of radial and tangential velocities:
（14）
two equations in the union type (14) obtain the true near point angle before forward fly-by
（15）
Will beTaking in formula (14), obtaining the eccentricity e of the next track which is reversely pushed, and obtaining the remaining speed of the next track according to the following formula:
（16）
in the method, in the process of the invention,for orbital angular momentum, determine near-wood point radius +.>；
According to the arch line rotation caused by the fly-over, the included angle difference between the eccentricity vectors of the two track sections can be obtained by the difference between true and near point angles before and after the fly-over:
（17）
in the method, in the process of the invention,for forward flying through the true near point angle of the front track,/->For the true near point angle of the orbit after forward flight, the eccentricity vector of the new orbit section is counterclockwise rotation of the original eccentricity vector around the orbit normal line +.>And (5) obtaining the track segment splicing.
As a preferred embodiment, the step S5 includes:
establishing a convergence coordinate system, wherein in the coordinate system, the origin is positioned at the mass center of the sun and the wood star, and the coordinate axes are arranged on the center of massxThe axis is pointed from the sun to the star,zthe axis coincides with the direction of angular momentum of the system,ythe shaft meets the right hand system;
the position of the spacecraft under the coordinate system is recorded as%x,y,z) The sun position is-0, 0), the position of the wooden star is (1->0, 0), the coordinates of the near-wood point in the convergence coordinate system are as follows:
（18）
in the method, in the process of the invention,is near the radius of wood point->Normalized values under a convergence coordinate system; the speed of the near wood point after the deceleration maneuver is perpendicular to the connecting line of the wood star and the near wood point, the direction of the orbit forward is selected, and the following is expressed in a convergence coordinate system:
（19）
wherein:，/>the included angle between the connecting line of the near wood point and the wood star and the x axis of the convergence coordinate system is represented, and the x axis is taken as the initial side and anticlockwise is positive.
As a preferred embodiment, the step S6 includes:
in a convergence coordinate system, the kinetic equation of the spacecraft is:
（20）
wherein:representation ofxWith respect to timetIs to ask for the help of (1)>Representing x with respect to timetIs the second derivation of->Representation ofyWith respect to timetIs to ask for the help of (1)>Representing y with respect to timetIs the second derivation of->Representing z with respect to timetIs a secondary derivative of (2); w represents an equivalent potential energy function, and the expression is as follows: /> （21）
Track recurrence from near wood point to far wood point is completed by using the method (20), and states at the far wood point are recorded asThe method comprises the following steps: />(22) Wherein->Representing the speed of the far wood point, v a Representation->Is a modulus of (2); />Represents the radius of the far wood point, r a Representation->Is a modulus of the model.
As a preferred embodiment, the step S7 includes:
obtaining the speed of the far wood pointAfter that, tangential maneuver is applied>Obtaining a new speed of the far wood point:
（23）
in the formula, v a Representation ofIs a modulus of (2); by means of the updated far wood point status +.>Recursion in the convergence coordinate system, and the next near wood point state is recorded as +.>The method comprises the following steps: />(24) And the near-wood point radius is equal to the desired near-wood point radius: />(25) Wherein->Representing the next near wood point speed, v p1 Representation->Is a modulus of (2); />Represents the radius of the next near wood point, r p1 Representation->Is a modulus of the model.
As a preferred embodiment, the step S8 includes:
capturing the track period by a given desireThe tangential speed reducer momentum required for decelerating from a large elliptical orbit to an elliptical orbit of a given period is analytically calculated in a two-body model by the following formula>：
（26）
In the formula, the superscript "-" indicates that the value is an unnormalized value, and can be obtained by performing inverse normalization operation on the normalized value under the convergence coordinate system.
As a preferred embodiment, the step S9 includes:
near wood point speed under the convergence coordinate system calculated according to the calculation of (19)Firstly, obtaining a reverse normalized near-wood point speed module value:
（27）
wherein the method comprises the steps ofNormalized units for speed;
the speed v of the near wood point before maneuver obtained according to the formula (3) p And the inverse normalized near-wood point velocity module value obtained by the methodFirst moment->Calculated by the following formula:
（28）
selecting proper optimized variable value to complete the track design by the optimized index J determined by the formula (29)
（29）
In the method, in the process of the invention,is->Inverse normalized values.
The invention has the beneficial effects that:
the method is suitable for track design and optimization of the wooden star capturing task; the novel capturing strategy is provided, and simultaneously, the capturing orbit is changed by utilizing the attraction of the natural satellite of the wooden star and the sun so as to meet different requirements in the capturing process, and a design scheme with higher precision can be provided for the given expected near-wooden point radius; when the wooden star capturing orbit is designed, compared with the traditional capturing scheme, the wooden star capturing orbit has obvious speed increment saving and partially meets the requirements of subsequent detection tasks.
Drawings
FIG. 1 is a schematic flow chart of a method for determining a woodstar capturing orbit of a deep space exploration spacecraft;
fig. 2 is a schematic diagram of a woody star capture orbit.
Detailed Description
The invention will be further described with reference to examples and drawings, to which reference is made, but which are not intended to limit the scope of the invention.
Referring to fig. 1, the method for determining the star capturing orbit of the deep space exploration spacecraft comprises the following steps:
step S1: establishing a design flow of a wooden star capturing orbit, selecting a variable optimization variable, and giving an expected orbit period after capturing and an expected orbit near wooden point radius after capturing;
step S2: determining calculation parameters of a wood guard attraction auxiliary process under the zero influence ball model;
step S3: according to the optimized variable and the auxiliary model of the wood Wei Yinli, a two-body problem analysis formula is utilized to reversely push the wood from a near-wood point to a wood guard flying place in time, so that the wood Wei Feiyue calculation is completed;
step S4: finishing the splicing of track segments before and after flying based on the calculated parameters before and after flying the wooden sanitation, continuing to push the wooden sanitation to the next flying place, and repeating the steps S3 and S4 or the step S4;
step S5: determining the position of the spacecraft at the near wood point and the speed and maneuvering speed increment of the spacecraft after first maneuvering based on the optimized variable;
step S6: the method comprises the steps of utilizing a circular limiting three-body dynamics model to recursively and backward in time from a near wood point, so as to determine the far wood point state of the spacecraft;
step S7: based on the remote wood point state of the spacecraft and the optimization variable, updating the remote wood point speed of the spacecraft after the second maneuver, and utilizing a circular limiting three-body dynamics model to recursively push the remote wood point state to the near wood point from the new remote wood point state in time, so as to determine the next near wood point state of the spacecraft;
step S8: according to the expected post-capture orbit period, and based on the next near-wood point state of the spacecraft, calculating by using a two-body problem model to obtain a third maneuvering speed increment;
step S9: and according to the speed increment required by the three maneuvers, comparing the relation between the radius of the next near-wood point and the radius of the expected near-wood point, and selecting the corresponding capturing track under the condition of the least consumption speed increment.
Taking fly-over wood Wei Si, wood guard three and final capture as a period of 200 days, a track design with a near wood point radius of Wei Sigui tracks is as follows:
step 1, selecting a variable optimization variable near-wood point diameter，r Eu And r Ga Revolution orbit radius, phase angle of two wood guard and three wood guard around wood star are respectively +.>Initial eccentricity->Residual speed at near wood point->And second time motor magnitude module value +.>As a variable optimization variable, a desired post-capture track period of 200 days and a desired post-capture track near-wood point radius of wood Wei Sigui track radius are given;
step 2, determining the orbit radius r of the orbit of the satellite to be flown over m =r Ga =107010 3 km; determining the residual speed of a hyperbolic orbit of a spacecraft around a wooden star +.>= 2.224km/s, near-wood point radius r p= 880700km, determining fly-by height h lfy =200km。
Step 3, firstly, according to a given near wood point radius r p And the residual speed at the near wood pointCalculating a hyperbolic track semi-long axis by the formula (1):
（1）
the eccentricity e can then be obtained directly and the near wood point velocity v calculated using the given residual velocity p ：
（2）
（3）
In the middle of=1.267127648/>10 8 Is the star gravitation constant;
according to the diameter of the near wood pointAnd near wood point velocity v p The orbital angular momentum module value can be obtained:
（4）
after the angular momentum modulus is obtained, the true near point angle can be passed according to the orbital equationTrack push was performed from 0 decrease:
（5）
when push back to r=r Ga Considered to be carrying out one gravitation assisted flying on the satellite, firstly according to the radius r of the three orbits of the wooden guard m Calculating to obtain the satellite speed:
（6）
the spacecraft with r=r can be obtained by the formula (3) m Velocity v at + I.e. the speed after the fly-by in the forward direction. Obtaining the hyperbolic orbit residual speed of the spacecraft flying around the wooden guard by using the cosine law:
（7）
in the method, in the process of the invention,for the flying path angle after forward flying, the calculation formula is as follows:
（8）
wherein a and e are the semi-long axis and the eccentricity of the hyperbolic orbit around the star respectively; the steering angle of the hyperbola of the spacecraft winding Wei Feiyue, namely the included angle between the arrival residual speed and the departure residual speed is calculated by the residual speed and the flying height:
（9）
wherein R is m =2634 km is the radius of kadsura,=9.8878/>10 3 km 3 /s 2 is the gravitation parameter of Muweisan, leaving the included angle between the residual speed and the satellite speed +.>The method is obtained by cosine theorem calculation:
（10）
angle between the remaining arrival speed and the satellite speedDetermined by the piecewise function:
（11）
the speed before forward fly-over and the flight path angle are obtained by the cosine law:
（12）。
step 4: determining the radial velocity v of a spacecraft before flying over a wooden guard r And tangential velocity：
（13）
Using another representation of radial and tangential velocities:
（14）
two equations in the union type (14) obtain the true near point angle before forward fly-by
（15）
Will beTaking in formula (14), obtaining the eccentricity e of the next track which is reversely pushed, and obtaining the remaining speed of the next track according to the following formula:
（16）
in the method, in the process of the invention,for orbital angular momentum, determine near-wood point radius +.>；
According to the arch line rotation caused by the fly-over, the included angle difference between the eccentricity vectors of the two track sections can be obtained by the difference between true and near point angles before and after the fly-over:
（17）
in the method, in the process of the invention,-0.7252, which is the true near point angle of the forward fly-over front trajectory; />= = -0.8345, the true near point angle of the track after forward fly-over; the eccentricity vector of the new track segment is the counterclockwise rotation of the original eccentricity vector around the normal line of the track +.>And (5) obtaining the track segment splicing.
Continuing by decreasing the true near point angleIs to push the track backward when r=r Ga And (3) repeating the steps (3) and (4) to calculate the track from three wood guard to four wood guard sections, and continuously reducing the true and near point angle +.>Then the sphere radius r=r is affected at the wood star soi Stopping the position, and completing the track design comprising the wooden sanitation flyover before the wooden point is approached.
In this embodiment, the remaining speed of the track segment flying last to the ball boundary is satisfied by changing the remaining speed of the first segment of track to be equal to the desired remaining speed of 5.6 km/s.
Step 5: establishing a convergence coordinate system, wherein in the coordinate system, the origin is positioned at the mass center of the sun and the wood star, and the coordinate axes are arranged on the center of massxThe axis is pointed from the sun to the star,zthe axis coincides with the direction of angular momentum of the system,ythe shaft meets the right hand system;
the position of the spacecraft under the coordinate system is recorded as%x,y,z) The sun position is-0, 0), the position of the wooden star is (1->0, 0), the coordinates of the near-wood point in the convergence coordinate system are as follows:
（18）
in the method, in the process of the invention,is near the radius of wood point->Normalized values under a convergence coordinate system; the speed of the near wood point after the deceleration maneuver is perpendicular to the connecting line of the wood star and the near wood point, the direction of the orbit forward is selected, and the following is expressed in a convergence coordinate system: />
（19）
Wherein:。
obtaining the position of the near wood point asSpeed is +.>。
Step 6: in a convergence coordinate system, the kinetic equation of the spacecraft is:
（20）
wherein:representation ofxWith respect to timetIs to ask for the help of (1)>Representing x with respect to timetIs the second derivation of->Representation ofyWith respect to timetIs to ask for the help of (1)>Representing y with respect to timetIs the second derivation of->Representing z with respect to timetIs a secondary derivative of (2); w represents an equivalent potential energy function, and the expression is as follows: /> （21）
Track recurrence from near wood point to far wood point is completed by using the method (20), and states at the far wood point are recorded asThe method comprises the following steps: />(22) Wherein->Representing the speed of the far wood point, v a Representation->Is a modulus of (2); />Represents the radius of the far wood point, r a Representation->Is a modulus of the model.
Obtaining the state of the far wood point as，/>。
Step 7: obtaining the speed of the far wood pointAfter that, tangential maneuver is applied>Obtaining a new speed of the far wood point:
（23）
in the formula, v a Representation ofIs a modulus of (2); by means of the updated far wood point status +.>Recursion in the convergence coordinate system, and the next near wood point state is recorded as +.>The method comprises the following steps: />(24) And the near-wood point radius is equal to the desired near-wood point radius: />(25) Wherein->Representing the next near wood point speed, v p1 Representation->Is a modulus of (2);represents the radius of the next near wood point, r p1 Representation->Is a modulus of the model.
This step is constraint solving by the fmincon solver of MATLAB.
Step 8: capturing the track period by a given desireBy the following publicly knownResolving and calculating tangential speed reducer momentum required by reducing the speed of a large elliptical orbit to an elliptical orbit with a given period under a two-body model>：
（26）
In the formula, the superscript "-" indicates that the value is an unnormalized value, and can be obtained by performing inverse normalization operation on the normalized value under the convergence coordinate system.
Step 9: near wood point speed under the convergence coordinate system calculated according to the calculation of (19)Firstly, obtaining a reverse normalized near-wood point speed module value:
（27）
wherein the method comprises the steps ofNormalized units for speed;
the speed v of the near wood point before maneuver obtained according to the formula (3) p And the inverse normalized near-wood point velocity module value obtained by the methodFirst moment->Calculated by the following formula:
（28）
selecting proper optimized variable value to complete the track design by the optimized index J determined by the formula (29)
（29）/>
In the method, in the process of the invention,is->Inverse normalized values.
In this example, the three maneuvers are 425.71m/s,8.20m/s,151.74m/s, respectively, only 8.20m/s speed increment is needed to lift the near wood point, the speed increment of the capturing desired elliptical orbit is 585.65m/s, and the capturing orbit height is no less than 880700km throughout.
According to the invention, by adopting a track design mode of combining the force of wood Wei Jie and the perturbation of solar attraction, the speed increment required by speed reduction and the speed increment required by lifting the near-wood point in the process of capturing the wooden star are reduced, and meanwhile, the high track near-wood point height can be maintained under certain conditions, so that the influence of wooden star radiation on a spacecraft is effectively avoided.
The present invention has been described in terms of the preferred embodiments thereof, and it should be understood by those skilled in the art that various modifications can be made without departing from the principles of the invention, and such modifications should also be considered as being within the scope of the invention.
Claims (10)
1. The method for determining the star capturing orbit of the deep space exploration spacecraft is characterized by comprising the following steps of:
step S1: selecting an optimization variable, and determining a period of the track expected to be captured and a radius of a near wood point of the track expected to be captured;
step S2: determining calculation parameters of a wood guard attraction auxiliary process under the zero influence ball model;
step S3: according to the optimization variable and the wooden sanitation attraction auxiliary process calculation parameter, a two-body problem analysis formula is utilized to reversely push the wooden sanitation flying from a near wooden point to a wooden sanitation flying position in time, and wooden sanitation flying calculation is completed to obtain wooden sanitation flying front and rear parameters;
step S4: finishing the splicing of track segments before and after flying based on the calculated parameters before and after flying the wooden sanitation, continuing to push the wooden sanitation to the next flying place, and repeating the steps S3 and S4 or the step S4;
step S5: determining the position of the spacecraft at the near wood point and the speed and maneuvering speed increment of the spacecraft after first maneuvering based on the optimized variable;
step S6: the method comprises the steps of utilizing a circular limiting three-body dynamics model to recursively and backward in time from a near wood point, so as to determine the far wood point state of the spacecraft;
step S7: based on the remote wood point state of the spacecraft and the optimization variable, updating the remote wood point speed of the spacecraft after the second maneuver, and utilizing a circular limiting three-body dynamics model to recursively push the remote wood point state to the near wood point from the new remote wood point state in time, so as to determine the next near wood point state of the spacecraft;
step S8: according to the expected post-capture orbit period, and based on the next near-wood point state of the spacecraft, calculating by using a two-body problem model to obtain a third maneuvering speed increment;
step S9: and according to the speed increment required by the three maneuvers, comparing the relation between the radius of the next near-wood point and the radius of the expected near-wood point, and selecting the corresponding capturing track under the condition of the least consumption speed increment.
2. The method according to claim 1, wherein the step S1 includes:
in the design of the capturing orbit, at least one auxiliary fly-over of wood Wei Yinli is contained in a section of hyperbolic orbit from a wood star influence ball to a near wood point, wherein the wood Wei Gongzhuai orbit is simplified into an ephemeris-free circular coplanar orbit, and the orbit calculation is simplified by utilizing a two-body problem analysis formula;
the orbit behind the near wood point is calculated by introducing solar attraction by using a circular limiting three-dimensional dynamics model, wherein the circular limiting three-dimensional dynamics model is used for dimensionless treatment of various units, MAnd M represents the solar mass and the wooden star mass respectively, M+m is taken as the mass unit, the average distance between the sun and the wooden star is taken as the unit length, the inverse of the orbit angular velocity of the sun and the wooden star is taken as the unit time,for the mass ratio of the system, +.>；
Selecting the diameter of the near wood pointPhase angle j, initial eccentricity +.>Residual speed at near wood point->And second time motor magnitude module value +.>As an optimization variable.
3. The method according to claim 1, wherein the step S2 includes:
determining the orbit radius of the satellite to be flown over around the orbit；
Determining the residual speed of a hyperbolic orbit of a spacecraft around a starNear wood point radius->；
Determining fly-by altitude。
4. The method according to claim 1, wherein the step S3 includes:
first according to a given near wood point diameterAnd the residual speed at the near wood point +.>Calculating a hyperbolic track semi-long axis by the formula (1):
（1）
in the method, in the process of the invention,is the constant of the attraction of the wooden star>=1.267127648/>10 8 ；
The eccentricity e can then be obtained directly and the near wood point velocity v calculated using the given residual velocity p ：
（2）
（3）
According to the diameter of the near wood pointAnd near wood point velocity v p The orbital angular momentum modulus h can be obtained:
（4）
after obtaining the angular momentum module value, according to the orbital equation, passing through the true near point angleTrack push was performed from 0 decrease:
（5）
wherein, h is the orbital angular momentum module value, e is the eccentricity, and r is the orbital radius;
when the orbit radius is the same as the orbit radius of the satellite to be flown, the satellite is regarded as carrying out a gravity assisted flying, and the satellite is firstly flown according to the orbit radius v m Calculating to obtain the satellite speed:
（6）
the near wood point diameter is reduced by the method (3)Changing to satellite orbit radius r m Residual speed at near wood point->Changing to the current track remaining speed +.>The spacecraft can be obtained at r=r m Velocity v at + I.e., the speed after the fly-by in the forward direction; obtaining the hyperbolic orbit residual speed of the spacecraft flying around the wooden guard by using the cosine law:
（7）
in the method, in the process of the invention,for the flying path angle after forward flying, the calculation formula is as follows:
（8）
wherein a and e are the semi-long axis and the eccentricity of the hyperbolic orbit around the star respectively; the steering angle of the hyperbola of the spacecraft winding Wei Feiyue, namely the included angle between the arrival residual speed and the departure residual speed is calculated by the residual speed and the flying height:
（9）
wherein R is m In order to fly over the radius of the satellite,is the gravitational parameter of the flying satellite; leaving the angle between the remaining speed and the satellite speed +.>The method is obtained by cosine theorem calculation:
（10）
angle between the remaining arrival speed and the satellite speedDetermined by the piecewise function:
（11）
the speed before forward fly-over and the flight path angle are obtained by the cosine law:
（12）。
5. the method according to claim 4, wherein the step S4 includes:
determining the radial velocity v of a spacecraft before flying over a wooden guard r And tangential velocity：
（13）
Using another representation of radial and tangential velocities:
（14）
two equations in the union type (14) obtain the true near point angle before forward fly-by
（15）
Will beTaking in formula (14), obtaining the eccentricity e of the next track which is reversely pushed, and obtaining the remaining speed of the next track according to the following formula:
（16）
in the method, in the process of the invention,for orbital angular momentum, determine near-wood point radius +.>；
According to the arch line rotation caused by the fly-over, the included angle difference between the eccentricity vectors of the two track sections can be obtained by the difference between true and near point angles before and after the fly-over:
（17）
in the method, in the process of the invention,for forward flying through the true near point angle of the front track,/->For the true near point angle of the orbit after forward flight, the eccentricity vector of the new orbit section is counterclockwise rotation of the original eccentricity vector around the orbit normal line +.>And (5) obtaining the track segment splicing.
6. The method according to claim 1, wherein the step S5 includes:
establishing a convergence coordinate system, wherein in the coordinate system, the origin is positioned at the mass center of the sun and the wood star, and the coordinate axes are arranged on the center of massxThe axis is pointed from the sun to the star,zthe axis coincides with the direction of angular momentum of the system,ythe shaft meets the right hand system;
the position of the spacecraft under the coordinate system is recorded as%x, y, z) The sun position is-0, 0), the position of the wooden star is (1->0, 0), the coordinates of the near-wood point in the convergence coordinate system are as follows:
（18）
in the method, in the process of the invention,is near the radius of wood point->Normalized values under a convergence coordinate system; the speed of the near wood point after the deceleration maneuver is perpendicular to the connecting line of the wood star and the near wood point, the direction of the orbit forward is selected, and the following is expressed in a convergence coordinate system:
（19）
wherein:,/>the included angle between the connecting line of the near wood point and the wood star and the x axis of the convergence coordinate system is represented, and the x axis is taken as the initial side and anticlockwise is positive.
7. The method according to claim 6, wherein the step S6 includes:
in a convergence coordinate system, the kinetic equation of the spacecraft is:
（20）
wherein:representation ofxWith respect to timetIs to ask for the help of (1)>Representing x with respect to timetIs the second derivation of->Representation ofyWith respect to timetIs to ask for the help of (1)>Representing y with respect to timetIs the second derivation of->Representing z with respect to timetIs a secondary derivative of (2); w represents an equivalent potential energy function, and the expression is as follows: /> （21）
Track recurrence from near wood point to far wood point is completed by using the method (20), and states at the far wood point are recorded asThe method comprises the following steps:(22) Wherein->Representing the speed of the far wood point, v a Representation->Is a modulus of (2); />Represents the radius of the far wood point, r a Representation ofIs a modulus of the model.
8. The method according to claim 7, wherein the step S7 includes:
obtaining the speed of the far wood pointAfter that, tangential maneuver is applied>Obtaining new far wood point speed +.>：
（23）
Using updated far wood point stateRecursion in the convergence coordinate system, and record the next near wood point state asThe method comprises the following steps: />(24) And the near-wood point radius is equal to the desired near-wood point radius: />(25) Wherein->Representing the next near wood point speed, v p1 Representation->Is a modulus of (2); />Indicating the nextRadius of near wood point, r p1 Representation->Is a modulus of the model.
9. The method according to claim 1, wherein said step S8 comprises:
capturing the track period by a given desireThe tangential speed reducer momentum required for decelerating from a large elliptical orbit to an elliptical orbit of a given period is analytically calculated in a two-body model by the following formula>：
（26）
In the formula, the superscript "-" indicates that the value is an unnormalized value, and is obtained by performing inverse normalization operation on the normalized value under the convergence coordinate system.
10. The method according to claim 6, wherein the step S9 includes:
near wood point speed under the convergence coordinate system calculated according to the calculation of (19)Firstly, obtaining a reverse normalized near-wood point speed module value:
（27）
wherein the method comprises the steps ofNormalized units for speed;
the speed v of the near wood point before maneuver obtained according to the formula (3) p And the inverse normalized near-wood point velocity module value obtained by the methodFirst moment->Calculated by the following formula:
（28）
selecting proper optimized variable value to complete the track design by the optimized index J determined by the formula (29)
（29）
In the method, in the process of the invention,is->Inverse normalized values.
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