CN113342044A - Ground track design method for tail end energy management section of reusable carrier - Google Patents
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Abstract
The invention provides a ground track design method for a terminal energy management section of a reusable vehicle, which comprises the steps of obtaining initial state parameters of an aircraft; determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section; determining a linear equation of a captured straight line segment; determining the position coordinates of the center of the HAC circle; and calculating the voyage of each flight section. According to the scheme of the invention, the detailed calculation sequence and the calculation method of the parameters of each stage of the ground track are determined according to the initial state information of the aircraft, the idea of ground track design is simplified, the shape of the ground track can be quickly and effectively changed by changing the radius of the HAC circle so as to adjust the course, and the turning angle of the captured turning section can be manually adjusted.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a ground track design method for a tail end energy management section of a reusable carrier.
Background
The Reusable Launch Vehicle (RLV) refers to a multipurpose aircraft which can be reused, can rapidly pass through the atmosphere, freely goes to and fro between the earth surface and the space, has the advantages of long-term on-orbit operation, ground return according to requirements, reusability and the like, can rapidly and conveniently transport effective loads to the space, realizes long-time on-orbit stop and maneuver, integrates an airplane, a satellite and a missile, is a novel Vehicle with military and civil dual-purpose aerospace technology highly integrated, has huge potential in commerce and military, and has wide application prospect and economic value.
The reusable vehicle mission profile includes an ascent segment, a rail entry segment, a rail on segment, a rail off segment, and a reentry return segment. The Reentry return segment can be divided into an initial Reentry segment (entry), a Terminal Area Energy Management segment (TAEM), and an Auto Landing segment (a & L). The terminal energy management section is connected with the initial reentry section and the automatic Landing section, and is an important flight stage before the RLV returns to a Landing field, and the main task of the stage is to dissipate redundant energy of the RLV and adjust the flight state after the initial reentry section is finished, so that the flight direction of the RLV is aligned to the runway direction and enters an automatic Landing window (ALI) with proper energy, and the terminal energy management section plays an important role in judging whether the RLV can reliably and efficiently complete horizontal Landing.
When the initial reentry section is finished, the state and energy of the RLV have great uncertainty, in order to ensure that the aircraft safely and accurately realizes horizontal landing, the redundant energy of the aircraft needs to be dissipated in the TAEM section, the mass of the RLV in the TAEM section is unchanged, and unit gravity energy is defined:
wherein E is aircraft energy; h is the flying height; v is the flight velocity; g is the acceleration of gravity; q is dynamic pressure; ρ is the atmospheric density.
The change rate of the unit gravity energy to the flight distance S can be obtained by the formula (1):
in the formula, SrefA reference area for the aircraft; cDIs a coefficient of resistance; and gamma is a flight path angle.
As can be seen from the equation (2), the energy of the RLV is monotonically decreased with the flight path, so that the total flight path can be changed by adjusting the shape parameter of the ground track, and the energy of the RLV can be adjusted to enable the RLV to enter the automatic landing window with proper energy. The RLV terminal energy management segment ground track is divided into a capture segment, a heading adjustment segment and a preliminary landing segment, and the three-dimensional schematic diagram and the ground track are respectively shown in FIG. 1 and FIG. 2.
As can be seen from fig. 1 and 2, the RLV ground flight size mainly depends on the initial position of the TAEM segment and the geometric parameters of the ground track of each stage. How to quickly calculate a set of feasible ground track parameters according to the current flight speed, the course angle and other parameters of the RLV and the energy size is the basis for realizing the horizontal landing of the RLV.
In the existing scheme, the radius of an HAC circle is set by a partial ground track design method, initial track geometric parameters of a capture section, a course adjustment section and a pre-landing section are obtained according to the initial state (position, yaw angle and speed) of an aircraft and parameters of the HAC circle, and the position of the HAC circle is iteratively corrected according to the RLV energy until the tail end energy constraint is met, so that the final ground track geometric parameters are determined. In part of methods, the position and radius of the HAC circle, the turning angle of the capture section and other trajectory parameters are used as iteration parameters, and feasible solutions meeting the terminal energy constraint are obtained through repeated iteration, so that the ground trajectory design is completed. In addition, the prior literature of the prior art hardly describes the calculation sequence and method of the trajectory geometric parameters (such as the turning angle and the turning center position of the capturing section) of each stage in detail.
Taking the TAEM online track generation method based on single parameter iteration as an example, the ground track geometric computation method designed by gomperbut et al is shown in fig. 3. In the method, the radius of the HAC circle is a given constant value, the coordinate of the circle center is selected according to the initial energy of the aircraft, if the energy is high, the high-energy HAC is selected, and if the energy is low, the low-energy HAC is selectedLow energy HAC, the method adjusts the ground range size, but the method does not describe the calculation method and sequence of the ground track geometric parameters of each stage in detail, namely the capture stage is turned by the angle psi1Center coordinates of turning and angle psi of turning of HAC section2The calculation method of (2) is not described.
The geometric calculation method of the ground track designed by the blue ocean et al is shown in fig. 4. The ground track geometric parameter calculation method is more common. According to the algorithm, the radius and the position coordinates of an HAC circle are given firstly, and the backstepping is carried out from a prepared landing segment according to geometric knowledge, so that the ground track geometric parameters of a course adjusting segment and a capturing segment are obtained gradually. In the calculation process, the tangent point coordinate corresponding to the initial position of the aircraft and the tangent line of the HAC circle is specified as the coordinate when the aircraft enters the HAC circle from the capturing section, and according to the assumptions, the parameters such as the turning angle of the course adjusting section, the turning radius of the capturing section, the turning center and the like are obtained by using the geometric relationship.
However, in the prior art, the calculation sequence and method of the ground track geometric parameters at each stage of the terminal energy management section are not described in detail in most cases. However, the TAEM section has a large number of key geometric parameters at each stage and affects each other, so that a person skilled in the art cannot clearly determine the determination sequence and the calculation method of the geometric parameters at each stage, and cannot obtain an accurate ground geometric trajectory. In part of the prior art, except that the determination sequence and the calculation method of the geometric parameters of each stage are not explicitly described, the mode of adjusting the ground voyage size is to select from a high-energy HAC circle, a standard HAC circle and a low-energy HAC circle, so that the ground voyage adjustable range is small, the adjustment precision is low, and the actual application requirements are difficult to meet. In the ground track, the straight line part of the capturing section is not tangent to the turning part of the capturing section and the HAC circle at the intersection point, as shown in FIG. 4, the straight line Rc is not tangent to the two turning arcs at the connecting point of the point N and the other end. The speed direction of the aircraft cannot change suddenly in the flying process, so that the ground track cannot be accurately tracked at two unrelated points, the control quantity can change suddenly, the actual range cannot be matched with the expected range, the design of a guidance control system is influenced, the construction of an executive machine is burdened, an error can be generated between the actual range and the estimated range, the control precision of energy control is reduced, and the flight mission fails. In other part of the prior art, geometric parameters (such as the position radius of the HAC circle, the turning radius angle of the capture section and the like) of each stage are used as optimization variables by the geometric locus calculation method, and a set of feasible parameters is obtained by designing complex iteration logic through multiple iterations to complete locus design. Even the key geometric parameters of each stage need to be incorporated into the iterative logic, and the iterative logic is complex due to a large number of iterative parameters, so that the calculation amount is large, and the design and the application of the algorithm are difficult.
Disclosure of Invention
In order to solve the technical problems, the invention provides a ground track design method for a tail end energy management section of a reusable carrier, and the method and the device are used for solving the problems that the calculation sequence and the method for the geometric parameters of the ground track at each stage of the tail end energy management section are not clear and the accurate ground geometric track cannot be obtained in the prior art; sudden changes in the control quantity and mismatching of the actual voyage with the expected voyage; the adjustment mode is solidified, and the flight requirement is not easy to meet.
According to a first aspect of the present invention, there is provided a method of reusable vehicle end energy management segment ground track design, the method comprising the steps of:
step S101: acquiring initial state parameters of an aircraft;
step S102: determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
step S103: determining a linear equation of a captured straight line segment;
step S104: determining the position coordinates of the center of the HAC circle;
step S105: and calculating the voyage of each flight section.
According to a second aspect of the present invention, there is provided a reusable vehicle end energy management section ground track design apparatus, the apparatus comprising:
an initial state acquisition module: configured to obtain initial state parameters of the aircraft;
a first calculation module: the method comprises the steps of determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
a second calculation module: configured to determine a captured straight line segment straight line equation;
a third calculation module: configured to determine HAC circle center position coordinates;
a fourth calculation module: and the method is configured to calculate each flight segment.
According to a third aspect of the invention, there is provided a reusable vehicle end energy management segment ground track design system comprising:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the plurality of instructions are for being stored by the memory and loaded and executed by the processor to perform the reusable vehicle end energy management segment ground track design method as previously described.
According to a fourth aspect of the present invention, there is provided a computer readable storage medium having a plurality of instructions stored therein; the plurality of instructions for loading and executing by the processor the reusable vehicle end energy management segment ground track design method as described above.
According to the scheme of the invention, the detailed calculation sequence and the calculation method of the parameters of each stage of the ground track are determined according to the initial state information of the aircraft, the ground track design problem is finally converted into the problem of searching for a circle tangent to two known straight lines, the idea of ground track design is simplified, the shape of the ground track can be quickly and effectively changed by changing the radius of the HAC circle so as to adjust the course, the course can be changed by adjusting the radius of the circle, and the turning angle of the captured turning section can be manually adjusted. The calculation mode, the calculation sequence and the calculation method for calculating the geometric parameters of each stage of the capturing turning section, the course adjusting section and the pre-landing section according to the initial state of the aircraft and the runway position are explained in detail, so that a complete and definite ground geometric trajectory is obtained. The size of the voyage is changed by adjusting the parameter of the radius of the HAC circle, the voyage can be continuously adjusted, the adjusting range is large, the adjusting mode is flexible, and the ground tracks meeting the voyage requirements can be obtained for different initial energy RLVs. In the ground tracks obtained by the ground track design method, the straight flight track is strictly tangent to the two sections of turning tracks, and the RLV has continuous speed direction change at the tangent point, so that the RLV can better track the ground tracks, the ground track tracking precision is improved, the error between the actual flight and the predicted flight is reduced, and the burden of an actuating mechanism and a guidance control system is reduced. The total range size is changed only by iterating the radius of the HAC circle, so that the problems of complexity, large calculated amount and the like caused by a multi-parameter iterative algorithm are solved. The turning radius of the captured turning section is determined according to the initial state parameters of the aircraft, and compared with a track design method for directly giving the turning radius, the method can effectively avoid the sudden change of the roll angle of the aircraft at the position and effectively reduce the burden of an actuating mechanism; the turning angle of the capturing turning section can be given according to actual requirements, and the flight direction of the aircraft at the capturing straight line section is determined, so that the flight direction of the aircraft at the stage can be adjusted according to actual conditions such as wind direction and the like, the resistance of the aircraft is changed, the energy of the aircraft can be better adjusted, and compared with a track design method for directly giving the turning angle, the method has the advantages of better robustness and higher engineering application value.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to implement them in accordance with the contents of the description, the following detailed description is given with reference to the preferred embodiments of the present invention and the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic three-dimensional trajectory of a terminal energy management segment;
FIG. 2 is a schematic diagram of a ground track for an end energy management segment;
FIG. 3 is a schematic diagram of a TAEM online trajectory generation method based on single-parameter iteration in the prior art;
FIG. 4 is a schematic diagram of a geometric generation method of a ground track in the prior art;
FIG. 5 is a schematic flow chart of a method for designing a ground track of an energy management section at the end of a reusable vehicle according to an embodiment of the present invention;
FIG. 6 is a schematic flow chart diagram of one embodiment of the present invention;
FIG. 7 is a schematic ground track view of an embodiment of the present invention;
FIG. 8 is a schematic view of a circle tangent to two straight lines at different radii for one embodiment of the present invention;
FIG. 9 is a block diagram of a ground track design apparatus for an end energy management section of a reusable vehicle according to an embodiment of the present invention.
Detailed Description
First, a flow of a ground track design method for an energy management section at the end of a reusable vehicle according to an embodiment of the present invention will be described with reference to fig. 5. As shown in fig. 5-6, the method comprises the steps of:
step S101: acquiring initial state parameters of an aircraft;
step S102: determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
step S103: determining a linear equation of a captured straight line segment;
step S104: determining the position coordinates of the center of the HAC circle;
step S105: and calculating the voyage of each flight section.
The step S101: obtaining an aircraft initial state parameter xm0,ym0,Vm0,γm0,ψm0Wherein x ism0As the abscissa of the initial moment of the aircraft, ym0Is the ordinate, V, of the aircraft at the initial momentm0For the velocity magnitude, psi, at the initial moment of the aircraftm0Is the course angle, gamma, of the aircraft at the initial momentm0The initial moment trajectory inclination angle of the aircraft is obtained;
as shown in fig. 7, xm0,ym0,Vm0,ψm0Respectively are the horizontal coordinate and the vertical coordinate of the aircraft at the initial moment, the speed of the aircraft at the initial moment and the course angle of the aircraft at the initial moment; x is the number ofac,yac,rac,ΔψacRespectively capturing the horizontal coordinate and the vertical coordinate of the circle center of the turning section, the turning radius of the turning section and the turning angle of the turning section; x is the number ofacf,yacf,ψ1Respectively capturing the horizontal coordinate, the vertical coordinate and the course angle when the turning section is finished; psitempCapturing the included angle between the connecting line of the circle center of the turning section and the position of the turning end point and the y axis; x is the number ofhac,yhac,rhac,ΔψhacThe horizontal and vertical coordinates of the center of the HAC circle, the radius of the HAC circle and the turning angle of the HAC circle are respectively; x is the number ofwp1,ywp1Respectively capturing a straight line l of the turning section1The horizontal and vertical coordinates of the tangent point of the HAC circle; the origin O is located at the beginning of the runway.
The step S102: determining the turning radius of the turning section, the course angle of the end point of the turning section, the circle center position of the turning section and the coordinates of the end position of the turning section, including:
step S1021: determining the turning radius r of the captured turning sectionac,
Wherein g is the acceleration of gravity, σacTo capture the mean roll angle of the turn section;
in this embodiment, σacThe value is 30-50 degrees.
Step S1022: determining an end point heading angle psi for capturing a turn1,
ψ1=ψm0-Δψac
Wherein, Delta psiacTo capture the turning angle of the turning section; psim0The course angle of the aircraft at the initial moment;
in this embodiment, the turning angle Δ ψ of the turning section is capturedacAccording to the actual situation, when the initial speed direction of the aircraft deviates from the runway direction to a large extent, the turning angle of the capturing turning section is given a large value, when the deviation degree is small, a small value can be given, and the minimum value can be 0.
Step S1023: determining the circle center position of the captured turning section and the coordinates of the end position of the captured turning section,
the circle center position of the turning section is captured as follows:
xac,yacrespectively capturing the horizontal and vertical coordinates of the circle center of the turning section,
calculating psitemp,ψtempIn order to capture the included angle between the connecting line of the circle center of the turning section and the position of the turning end point and the y axis:
the coordinates of the end point of the captured turning segment are:
xacf,yacfrespectively the abscissa and ordinate at the end of the acquisition turn section.
The step S103: determining a captured straight line segment linear equation comprising:
capturing the straight line segment with the equation of y-k1x+b1In the formula, k1Is a slope, b1Is the intercept of the beam, wherein,
in this embodiment, a straight line segment l is captured1Tangent to both the arc of the capturing turn section and the HAC circle1Passing point (x)acf,yacf) At an angle psi to the x-axis1。
The step S104: determining HAC circle center position coordinates, comprising:
the longitudinal coordinate of the center of the HAC circle is as follows:
yhac=rhac
the abscissa of the center of the HAC circle is as follows:
rhacis the HAC circle radius.
In this embodiment, the HAC circle and the straight line l of the capturing straight line segment1And runway centerline l2Are all tangent, the previous step has obtained1The linear equation of (a); the track centerline l is due to the coordinate dots at the start of the track2Is the x-axis. At this time, it is converted into finding a simultaneous word and a1,l2Tangent circles, and thus for every given HAC circle radius, a satisfactory HAC circle coordinate is determined, as shown in fig. 8.
The step S105: calculating each flight segment, including:
capturing turn section voyage SactCapturing straight line segment voyage SacsHAC turn section voyage ShacThe calculation formula is as follows:
in the formula,. DELTA.psihac=360-ψ1The angle of the HAC turning section is shown.
The track can determine different track shapes by adjusting the radius of the HAC circle, so that the range size is adjusted, and the requirements of aircrafts with different energies on the range are met.
An embodiment of the present invention further provides a ground track design apparatus for an energy management section at an end of a reusable vehicle, as shown in fig. 9, the apparatus includes:
an initial state acquisition module: configured to obtain initial state parameters of the aircraft;
a first calculation module: the method comprises the steps of determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
a second calculation module: configured to determine a captured straight line segment straight line equation;
a third calculation module: configured to determine HAC circle center position coordinates;
a fourth calculation module: and the method is configured to calculate each flight segment.
The embodiment of the invention further provides a ground track design system for the tail end energy management section of the reusable vehicle, which comprises the following steps:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the plurality of instructions are for being stored by the memory and loaded and executed by the processor to perform the reusable vehicle end energy management segment ground track design method as previously described.
The embodiment of the invention further provides a computer readable storage medium, wherein a plurality of instructions are stored in the storage medium; the plurality of instructions for loading and executing by the processor the reusable vehicle end energy management segment ground track design method as described above.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
In the embodiments provided in the present invention, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions in actual implementation, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.
The integrated unit implemented in the form of a software functional unit may be stored in a computer readable storage medium. The software functional unit is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a physical machine server, or a network cloud server, etc., and needs to install a Ubuntu operating system) to perform some steps of the method according to various embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent change and modification made to the above embodiment according to the technical spirit of the present invention are still within the scope of the technical solution of the present invention.
Claims (10)
1. A method for ground track design of an end energy management segment of a reusable vehicle, the method comprising the steps of:
step S101: acquiring initial state parameters of an aircraft;
step S102: determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
step S103: determining a linear equation of a captured straight line segment;
step S104: determining the position coordinates of the center of the HAC circle;
step S105: and calculating the voyage of each flight section.
2. The method for ground track design of an end energy management segment of a reusable vehicle as claimed in claim 1, wherein the step S101: obtaining an aircraft initial state parameter xm0,ym0,Vm0,γm0,ψm0Wherein x ism0As the abscissa of the initial moment of the aircraft, ym0Is the ordinate, V, of the aircraft at the initial momentm0Is the speed magnitude of the aircraft at the initial moment, gammam0For the initial moment of the aircraft ballistic inclination angle, psim0Is the course angle of the aircraft at the initial moment.
3. The method for ground track design of an end energy management segment of a reusable vehicle as claimed in claim 2, wherein the step S102 comprises:
step S1021: determining the turning radius r of the captured turning sectionac,
Wherein g is the acceleration of gravity, σacTo be caughtObtaining the average rolling angle of the turning section;
step S1022: determining an end point heading angle psi for capturing a turn1,
ψ1=ψm0-Δψac
Wherein, Delta psiacTo capture the turning angle of the turning section; psim0The course angle of the aircraft at the initial moment;
step S1023: determining the circle center position of the captured turning section and the coordinates of the end position of the captured turning section,
the circle center position of the turning section is captured as follows:
xac,yacrespectively capturing the horizontal and vertical coordinates of the circle center of the turning section,
calculating psitemp,ψtempIn order to capture the included angle between the connecting line of the circle center of the turning section and the position of the turning end point and the y axis:
the coordinates of the end point of the captured turning segment are:
xacf,yacfrespectively the abscissa and ordinate at the end of the acquisition turn section.
4. The method for ground track design of an end energy management segment of a reusable vehicle as claimed in claim 3, wherein the step S103 comprises:
capturing the straight line segment with the equation of y-k1x+b1In the formula, k1Is a slope, b1Is the intercept of the beam, wherein,
in this embodiment, a straight line segment l is captured1Tangent to both the arc of the capturing turn section and the HAC circle1Passing point (x)acf,yacf) At an angle psi to the x-axis1。
5. The method for ground track design of an end energy management segment of a reusable vehicle as claimed in claim 4, wherein the step S104: determining HAC circle center position coordinates, comprising:
the longitudinal coordinate of the center of the HAC circle is as follows:
yhac=rhac
the abscissa of the center of the HAC circle is as follows:
rhacis the HAC circle radius.
6. The method for ground track design of an end energy management segment of a reusable vehicle as claimed in claim 5, wherein the step S105: calculating each flight segment, including:
capturing turn section voyage SactCapturing straight line segment voyage SacsHAC turn section voyage ShacThe calculation formula is as follows:
in the formula,. DELTA.psihac=360-ψ1The angle of the HAC turning section is shown.
7. An apparatus for ground track design of an end energy management section of a reusable vehicle, the apparatus comprising:
an initial state acquisition module: configured to obtain initial state parameters of the aircraft;
a first calculation module: the method comprises the steps of determining a turning radius of a captured turning section, a course angle of an end point of the captured turning section, a circle center position of the captured turning section and coordinates of the end position of the captured turning section;
a second calculation module: configured to determine a captured straight line segment straight line equation;
a third calculation module: configured to determine HAC circle center position coordinates;
a fourth calculation module: and the method is configured to calculate each flight segment.
8. The reusable vehicle end energy management segment ground track design apparatus of claim 7, wherein the initial state acquisition module: for obtaining initial state parameter x of aircraftm0,ym0,Vm0,γm0,ψm0Wherein x ism0As the abscissa of the initial moment of the aircraft, ym0Is the ordinate, V, of the aircraft at the initial momentm0For the velocity magnitude, psi, at the initial moment of the aircraftm0Is the course angle, gamma, of the aircraft at the initial momentm0The initial moment ballistic inclination angle of the aircraft.
9. A reusable vehicle end energy management segment ground track design system, comprising:
a processor for executing a plurality of instructions;
a memory to store a plurality of instructions;
wherein the plurality of instructions for storage by the memory and loading and executing by the processor the reusable vehicle end energy management segment ground track design method of any of claims 1-6.
10. A computer-readable storage medium having stored therein a plurality of instructions; the plurality of instructions for loading and executing by a processor the reusable vehicle end energy management segment ground track design method of any of claims 1-6.
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