CN110222412A - A kind of calculation method of spacecraft return trajectory analytic gradient - Google Patents

A kind of calculation method of spacecraft return trajectory analytic gradient Download PDF

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CN110222412A
CN110222412A CN201910472929.7A CN201910472929A CN110222412A CN 110222412 A CN110222412 A CN 110222412A CN 201910472929 A CN201910472929 A CN 201910472929A CN 110222412 A CN110222412 A CN 110222412A
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voyage
gradient
relational expression
braking
angle
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CN110222412B (en
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陈伟跃
黄震
马晓兵
张治国
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Beijing Space Technology Research and Test Center
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Beijing Space Technology Research and Test Center
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Abstract

The present invention relates to a kind of calculation methods of spacecraft return trajectory analytic gradient, comprising: S1. establishes spacecraft return trajectory retaining segment voyage Sb1With braking duration tpThe first relational expression, and according to the first relational expression obtain retaining segment voyage Sb1To braking duration tpFirst gradient；S2. spacecraft return trajectory coasting-flight phase voyage S is establishedb2With braking duration tpThe second relational expression, and according to the second relational expression obtain coasting-flight phase voyage Sb2To braking duration tpThe second gradient；S3. spacecraft return trajectory reentry stage voyage S is establishedb3With braking duration tpThird relational expression, and according to third relational expression obtain reentry stage voyage Sb3To braking duration tp3rd gradient；S4. it sums to first gradient, the second gradient and 3rd gradient and obtains the total voyage S of return trajectorybTo braking duration tpGradient.The present invention effectively reduces the number of iterations during Entry trajectory design, and then improves the calculating and design efficiency of return trajectory.

Description

A kind of calculation method of spacecraft return trajectory analytic gradient
Technical field
The present invention relates to a kind of calculation methods of spacecraft return trajectory more particularly to a kind of spacecraft return trajectory to parse The calculation method of gradient.
Background technique
Return refers to that spacecraft enters earth atmosphere along transition track along its running track or after becoming rail, in sky The process slowed down under the action of aerodynamic force and landed.Running track of the spacecraft in return course is known as return trajectory.Near-earth The return trajectory of spacecraft can be divided into posture adjustment section, retaining segment, coasting-flight phase, reentry stage and landing phase, dynamics used by every section Model is different, and calculating process is more complicated.Since spacecraft is in return course, reenter leads to that Aerodynamic Heating is serious, ring at a high speed Border is severe, and deceleration overload, Aerodynamic Heating bring hot-fluid and the total caloric receptivity and landing precision for reentering process are to return to rail The constraint condition of road design.Therefore, the design of return trajectory generally uses iterative process, obtains meeting constraint by iterative calculation The nominal return trajectory of condition is realized and returns to track optimizing and provide for the design of the related systems such as solar heat protection, structure, control and propulsion Technical parameter.
Existing Entry trajectory design method generally uses numerical gradient to be iterated calculating.Under normal conditions, with braking Point and braking duration as iteration variable, using the location error of reentry angle and parachute-opening point as iterative target, using numerical gradient Carry out return trajectory iterative calculation.When being calculated using numerical gradient, the influence of iterative initial value and gradient guess value to the number of iterations It is larger, need multiple tentative calculation that can just select suitable gradient magnitude, the calculation times of return trajectory are more, single return trajectory For the convergence rate of calculating compared with slow, the number of iterations is more, Entry trajectory design and computational efficiency are low.
Summary of the invention
The purpose of the present invention is to provide a kind of calculation methods of spacecraft return trajectory analytic gradient, solve spacecraft and return Return the low problem of Track desigh computational efficiency.
For achieving the above object, the present invention provides a kind of calculation method of spacecraft return trajectory analytic gradient, packet It includes:
S1. spacecraft return trajectory retaining segment voyage S is establishedb1With braking duration tpThe first relational expression, and according to described First relational expression obtains the retaining segment voyage Sb1To the braking duration tpFirst gradient；
S2. spacecraft return trajectory coasting-flight phase voyage S is establishedb2With the braking duration tpThe second relational expression, and according to Second relational expression obtains the coasting-flight phase voyage Sb2To the braking duration tpThe second gradient；
S3. spacecraft return trajectory reentry stage voyage S is establishedb3With the braking duration tpThird relational expression, and according to The third relational expression obtains the reentry stage voyage Sb3To the braking duration tp3rd gradient；
S4. the return trajectory is obtained to the summation of the first gradient, second gradient and the 3rd gradient always to navigate Journey SbTo the braking duration tpGradient.
According to an aspect of the present invention, in step S1, it is assumed that the spacecraft is extremely made in the braking starting point of retaining segment The orbit angular velocity of dynamic end point is consistent, then first relational expression are as follows:
Wherein, h0For the orbital angular momentum of braking point, Rd0For the geocentric distance of braking point, RpFor earth mean orbit half Diameter, hfFor the height of parachute-opening point.
According to an aspect of the present invention, in step S2, comprising:
S21. the spacecraft is obtained in the end point velocity inertial V of end of braking point position0In local horizontal component Vx With radial component Vy；
S22. according to the horizontal component VxWith the radial component VyObtain the end point velocity inertial V0, Yi Jisuo State velocity inertial V0Velocity inertial inclination angle theta0；
S23. according to the end point velocity inertial V0With the velocity inertial inclination angle theta0The spacecraft is obtained in coasting-flight phase Coasting-flight phase voyage angle
S24. according to the coasting-flight phase voyage Sb2, the braking duration tpWith coasting-flight phase voyage angle ψbEstablish described Two relational expressions；
S25. according to second relational expression, second gradient is calculated using chain type Rule for derivation.
According to an aspect of the present invention, in step S21, it is assumed that retro-speed increment is pulse, and position is in the system The midpoint of section is moved, then horizontal component VxAre as follows:
Radial component VyAre as follows:
Wherein, Vi0For the brake inertia speed of braking point, θiFor the speed inclination angle of braking point velocity inertial, Δ ν is braking Speed increment, ψzFor braking pitch angle and-π≤ψz< π.
According to an aspect of the present invention, in step S23, coasting-flight phase voyage angleAre as follows:
Coefficient in expression formula are as follows:
A=2Re(1+tan2θ0)-(Rd0+Re)ν0,
B=Reν0tanθ0,
C=(Rd0-Re)ν0,
Wherein, μ is Gravitational coefficient of the Earth, ReFor the geocentric distance of reentry point.
According to an aspect of the present invention, in step S25, comprising:
S251 calculates coasting-flight phase voyage anglePartial derivative to coefficient in second relational expression and described Coefficient is to the end point velocity inertial V in two relational expressions0With the velocity inertial inclination angle theta0Partial derivative；
S252. the end point velocity inertial V is calculated separately0With the velocity inertial inclination angle theta0To the end point inertia Speed V0In local horizontal component VxWith radial component VyPartial derivative；
S253. the end point velocity inertial V is calculated0In local horizontal component VxWith radial component VyTo the braking The partial derivative of speed increment Δ ν and the retro-speed increment Delta ν are to the braking duration tpPartial derivative；
According to an aspect of the present invention, in step S3, comprising:
S31. the retaining segment voyage angle δ of the spacecraft retaining segment is obtainedb, the orbital eccentricity of the spacecraft coasting-flight phase The orbital angular momentum h of e and coasting-flight phase；
S32. according to retaining segment voyage angle δb, the orbital eccentricity e, the orbital angular momentum h and described slide The angle Duan Hangcheng ψbObtain the reentry angle θ of spacecrafte；
S33. according to the reentry stage voyage Sb3, the braking duration tp, the reentry angle θeWith spacecraft in parachute-opening point Speed inclination angle thetafEstablish the third relational expression；
S34. according to the third relational expression, the 3rd gradient is calculated using chain type Rule for derivation.
According to an aspect of the present invention, in step S32, retaining segment voyage angle δbAre as follows:
The orbital eccentricity e are as follows:
The orbital angular momentum h are as follows:
H=Rd0V0cosθ0,
The reentry angle θeAre as follows:
According to an aspect of the present invention, in step S34, comprising:
S341. retaining segment voyage angle δ is calculatedbTo the braking duration tpPartial derivative；
S342. the orbital eccentricity e and the orbital angular momentum h are calculated to the end point velocity inertial V0With it is described Velocity inertial inclination angle theta0Partial derivative；
S343. reentry angle θ is calculatedeTo the orbital eccentricity e, retaining segment voyage angle δb, coasting-flight phase voyage angle ψb, the orbital angular momentum h partial derivative；
S344. the reentry stage voyage S is calculatedb3To the reentry angle θeWith the parachute-opening spot speed inclination angle thetafLocal derviation Number；
S345. the parachute-opening spot speed inclination angle theta is calculatedfTo the reentry angle θePartial derivative.
According to an aspect of the present invention, in step S344, the reentry stage voyage S is constructedb3With the reentry angle θeWith The parachute-opening spot speed inclination angle thetafThe 4th relational expression, the reentry stage voyage S is calculated based on the 4th relational expressionb3To described Reentry angle θeWith the parachute-opening spot speed inclination angle thetafPartial derivative；
4th relational expression are as follows:
Wherein, β is atmospheric density ρ to the gradient of height H and the ratio of atmospheric density, i.e.,
A kind of scheme according to the present invention calculates voyage to the gradient of braking duration, different using analytical expression Under rail conditions design return trajectory when, using can accurately be obtained when analytic gradient expression formula voyage to braking duration ladder Degree avoids the tentative calculation process that numerical gradient is constantly artificially adjusted when carrying out return trajectory calculating using numerical gradient guess value, The return trajectory calculation times during Entry trajectory design are effectively reduced, the convergence rate of iterative calculation, single are improved Return trajectory calculating can be obtained the return trajectory met the requirements, improve the calculating and design efficiency of return trajectory.
Detailed description of the invention
Fig. 1 schematically shows a kind of step frame of the calculation method of spacecraft return trajectory analytic gradient according to the present invention Figure.
Specific embodiment
It, below will be to embodiment in order to illustrate more clearly of embodiment of the present invention or technical solution in the prior art Needed in attached drawing be briefly described.It should be evident that the accompanying drawings in the following description is only of the invention some Embodiment for those of ordinary skills without creative efforts, can also be according to these Attached drawing obtains other attached drawings.
When being described for embodiments of the present invention, term " longitudinal direction ", " transverse direction ", "upper", "lower", " preceding ", " rear ", "left", "right", "vertical", "horizontal", "top", "bottom" "inner", orientation or positional relationship expressed by "outside" are based on phase Orientation or positional relationship shown in the drawings is closed, is merely for convenience of description of the present invention and simplification of the description, rather than instruction or dark Show that signified device or element must have a particular orientation, be constructed and operated in a specific orientation, therefore above-mentioned term cannot It is interpreted as limitation of the present invention.
The present invention is described in detail with reference to the accompanying drawings and detailed description, embodiment cannot go to live in the household of one's in-laws on getting married one by one herein It states, but therefore embodiments of the present invention are not defined in following implementation.
As shown in Figure 1, a kind of embodiment according to the present invention, a kind of spacecraft return trajectory analytic gradient of the invention Calculation method, comprising:
S1. spacecraft return trajectory retaining segment voyage S is establishedb1With braking duration tpThe first relational expression, and according to first Relational expression obtains retaining segment voyage Sb1To braking duration tpFirst gradient；
S2. spacecraft return trajectory coasting-flight phase voyage S is establishedb2With braking duration tpThe second relational expression, and according to second Relational expression obtains coasting-flight phase voyage Sb2To braking duration tpThe second gradient；
S3. spacecraft return trajectory reentry stage voyage S is establishedb3With braking duration tpThird relational expression, and according to third Relational expression obtains reentry stage voyage Sb3To braking duration tp3rd gradient；
S4. it sums to first gradient, the second gradient and 3rd gradient and obtains the total voyage S of return trajectorybTo braking duration tp's Gradient.
A kind of embodiment according to the present invention, the return of spacecraft refer to spacecraft along its running track or by becoming Enter earth atmosphere along transition track after rail, the process slowed down and landed under the action of air force.In present embodiment In, it returns since braking, experienced braking, slides and reenter three phases.Enable retaining segment, coasting-flight phase and three sections of reentry stage Voyage is respectively as follows: Sb1、Sb2、Sb3, total voyage is Sb, when braking a length of tp。
A kind of embodiment according to the present invention, track weather is slower in the height change of retaining segment, thus, it is supposed that braking The orbit angular velocity of starting point to end of braking point is uniformly constant, retaining segment voyage Sb1It can be expressed as:
Wherein, h0For the orbital angular momentum of braking point, Rd0For the geocentric distance of braking point, RpFor earth mean orbit half Diameter, hfFor the height of parachute-opening point.
Deformation can be then carried out to it according to above-mentioned formula (1) and obtains retaining segment voyage Sb1To braking duration tpFirst ladder Degree, first gradient indicate are as follows:
According to the present invention, under impulse orbit transfer model, the voyage of retaining segment is 0, can not real embodiment retaining segment boat The drawbacks of actual moving process of its device, the present invention can establish limited engine thrust situation by using above-mentioned calculation Under accurate brake model.For impulse orbit transfer, model accuracy is higher, to the analytic gradient meter of spacecraft return trajectory It is more accurate to calculate, and then advantageously to the careful design of spacecraft return trajectory.
A kind of embodiment according to the present invention, in step S2, comprising:
S21. spacecraft is obtained in the end point velocity inertial V of end of braking point0In local horizontal component VxWith radial point Measure Vy.In the present embodiment, it is assumed that retro-speed increment is pulse, and position is at the midpoint of retaining segment, in present embodiment In, spacecraft will move one section of segmental arc, and the accumulation of brake engine booting a period of time in orbit in braking process Effect is retro-speed increment Delta ν.In conventional impulse orbit transfer model, spacecraft obtains impulse speed in braking point moment and increases Amount, retaining segment voyage are 0, and the simplification degree of model is larger.In the present invention, by the braking process in the case of limited engine thrust Equivalent process has been carried out, has mathematically thought that the speed increment of braking process generation acts on the middle position of retaining segment, it may be assumed that make With point at the midpoint of retaining segment.The booting starting point of practical brake engine is carried out in retaining segment starting point, but in process of mathematical modeling Equivalent process.By equivalent process, retaining segment is depicted there are this actual physics process of voyage, model accuracy is than conventional mould Type is higher.
Then horizontal component VxAre as follows:
Radial component VyAre as follows:
Wherein, Vi0For the velocity inertial of braking point, θiFor the velocity inertial inclination angle of braking point, Δ ν is retro-speed increment, ψzFor braking pitch angle and-π≤ψz< π.
S22. according to horizontal component VxWith radial component VyObtain end point velocity inertial V0And velocity inertial V0It is used Property speed inclination angle theta0.In the present embodiment, end point velocity inertial V0Are as follows:
Velocity inertial inclination angle theta0Are as follows:
θ0=arctan (Vy/Vx) (6)。
S23. according to end point velocity inertial V0With velocity inertial inclination angle theta0Spacecraft is obtained in the coasting-flight phase voyage of coasting-flight phase AngleIn the present embodiment, coasting-flight phase voyage angleAre as follows:
Coefficient in expression formula is,
A=2Re(1+tan2θ0)-(Rd0+Re)ν0(8),
B=Reν0tanθ0(9),
C=(Rd0-Re)ν0(10),
Wherein, μ is Gravitational coefficient of the Earth, ReFor the geocentric distance of reentry point.
S24. according to coasting-flight phase voyage Sb2, braking duration tpWith coasting-flight phase voyage angleEstablish the second relational expression.In this reality It applies in mode, the second relational expression can indicate are as follows:
S25. according to the second relational expression, the second gradient is calculated using chain type Rule for derivation.In the present embodiment, comprising:
S251 calculates coasting-flight phase voyage angleCoefficient in partial derivative and the second relational expression to coefficient in the second relational expression To end point velocity inertial V0With velocity inertial inclination angle theta0Partial derivative；In the present embodiment, it is calculated and is slided according to formula (7) The angle Duan HangchengTo the partial derivative of coefficient a, b, c in the second relational expression, that is, may be expressed as:
It is fast to end point inertia that coefficient a, b, c in the second relational expression are calculated separately according to formula (8), (9), (10) and (11) Spend V0With velocity inertial inclination angle theta0Partial derivative, that is, may be expressed as:
S252. end point velocity inertial V is calculated separately0With velocity inertial inclination angle theta0To end point velocity inertial V0In locality Horizontal component VxWith radial component VyPartial derivative.In the present embodiment, it is calculated separately according to formula (3), (4), (5) and (6) End point velocity inertial V0With velocity inertial inclination angle theta0To end point velocity inertial V0In local horizontal component VxWith radial component Vy Partial derivative, that is, may be expressed as:
S253. end point velocity inertial V is calculated0In local horizontal component VxWith radial component VyTo retro-speed increment The partial derivative and retro-speed increment Delta ν of Δ ν is to braking duration tpPartial derivative.In the present embodiment, according to formula (3), (4) calculate end point velocity inertial V0In local horizontal component VxWith radial component VyTo the inclined of retro-speed increment Delta ν Derivative may be expressed as:
Retro-speed increment Delta ν is calculated to braking duration tpPartial derivative, that is, may be expressed as:
Wherein, n is the number of units of brake engine, and F is the thrust of brake engine, ApFor the thrust and boat of brake engine The angle of its body axis, IspFor the specific impulse of brake engine, m0For the initial mass of spacecraft.
In the present embodiment, the above-mentioned partial derivative being calculated is added sequentially to the second relationship with chain type Rule for derivation In formula, to calculate the second gradient.
It, can be accurate using calculation of the invention to different return preliminary orbit conditions according to according to the present invention Reflect under different rail conditions and brake the influence that duration changes voyage, avoids the examination repeatedly of constantly adjustment conjecture numerical gradient Calculation process.
A kind of embodiment according to the present invention, in step S3, comprising:
S31. the retaining segment voyage angle δ of spacecraft retaining segment is obtainedb, the orbital eccentricity e of spacecraft coasting-flight phase, and it is sliding The orbital angular momentum h of row section.In the present embodiment, retaining segment voyage angle δbAre as follows:
Orbital eccentricity e are as follows:
Orbital angular momentum h are as follows:
H=Rd0V0cosθ0 (15)。
S32. according to retaining segment voyage angle δb, orbital eccentricity e, orbital angular momentum h and coasting-flight phase voyage angleObtain boat The reentry angle θ of its devicee.In the present embodiment, reentry angle θeAre as follows:
S33. according to reentry stage voyage Sb3, braking duration tp, reentry angle θeWith spacecraft parachute-opening point speed inclination angle thetafIt builds Vertical third relational expression.In the present embodiment, third relational expression are as follows:
S34. according to third relational expression, 3rd gradient is calculated using chain type Rule for derivation.In the present embodiment, comprising:
S341. reentry angle θ is calculatedeTo orbital eccentricity e, retaining segment voyage angle δb, coasting-flight phase voyage angleTrack angular motion Measure the partial derivative of h.In the present embodiment, reentry angle θ is calculated according to formula (16)eTo orbital eccentricity e, retaining segment voyage angle δb, coasting-flight phase voyage angleThe partial derivative of orbital angular momentum h can indicate are as follows:
S342. retaining segment voyage angle δ is calculatedbTo braking duration tpPartial derivative.In the present embodiment, retaining segment voyage Angle δbTo braking duration tpPartial derivative indicate are as follows:
S343. orbital eccentricity e and orbital angular momentum h is calculated to end point velocity inertial V0With velocity inertial inclination angle theta0's Partial derivative.In the present embodiment, orbital eccentricity e and orbital angular momentum h is calculated to end point according to formula (11) and (14) Velocity inertial V0With velocity inertial inclination angle theta0Partial derivative, can indicate are as follows:
S344. reentry stage voyage S is calculatedb3To reentry angle θeWith parachute-opening spot speed inclination angle thetafPartial derivative.In this embodiment party In formula, reentry stage voyage S is constructedb3With reentry angle θeWith parachute-opening spot speed inclination angle thetafThe 4th relational expression, be based on the 4th relational expression Calculate reentry stage voyage Sb3To reentry angle θeWith parachute-opening spot speed inclination angle thetafPartial derivative；
4th relational expression are as follows:
Wherein, β is atmospheric density ρ to the gradient of height H and the ratio of atmospheric density.β can be indicated are as follows:
S345. parachute-opening spot speed inclination angle theta is calculatedfTo reentry angle θePartial derivative.In the present embodiment, it is closed according to the 4th It is that formula calculates parachute-opening spot speed inclination angle thetafTo reentry angle θePartial derivative, can indicate are as follows:
In the present embodiment, the above-mentioned partial derivative being calculated is added sequentially to third relationship with chain type Rule for derivation In formula, to calculate 3rd gradient.
A kind of embodiment according to the present invention, summing to obtain to first gradient, the second gradient and 3rd gradient returns to rail The total voyage S in roadbTo braking duration tpGradient.In present embodiment, total voyage SbWith braking duration tpGradient relation can table It is shown as:
According to the present invention, different return preliminary orbit conditions can be accurately reflected using calculation of the invention The influence that duration changes voyage is braked under different rail conditions, avoids the tentative calculation repeatedly of constantly adjustment conjecture numerical gradient Journey.
Above content is only the example of concrete scheme of the invention, for the equipment and structure of wherein not detailed description, is answered When being interpreted as that the existing common apparatus in this field and universal method is taken to be practiced.
The foregoing is merely a schemes of the invention, are not intended to restrict the invention, for the technology of this field For personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.

Claims (10)

1. a kind of calculation method of spacecraft return trajectory analytic gradient, comprising:
S1. spacecraft return trajectory retaining segment voyage S is establishedb1With braking duration tpThe first relational expression, and according to described first Relational expression obtains the retaining segment voyage Sb1To the braking duration tpFirst gradient；
S2. spacecraft return trajectory coasting-flight phase voyage S is establishedb2With the braking duration tpThe second relational expression, and according to described Second relational expression obtains the coasting-flight phase voyage Sb2To the braking duration tpThe second gradient；
S3. spacecraft return trajectory reentry stage voyage S is establishedb3With the braking duration tpThird relational expression, and according to described Third relational expression obtains the reentry stage voyage Sb3To the braking duration tp3rd gradient；
S4. the total voyage S of return trajectory is obtained to the summation of the first gradient, second gradient and the 3rd gradientbIt is right The braking duration tpGradient.
2. calculation method according to claim 1, which is characterized in that in step S1, it is assumed that the spacecraft is in retaining segment The orbit angular velocity of braking starting point to end of braking point be consistent, then first relational expression are as follows:
Wherein, h0For the orbital angular momentum of braking point, Rd0For the geocentric distance of braking point, RpFor earth mean orbit radius, hfFor The height of parachute-opening point.
3. calculation method according to claim 2, which is characterized in that in step S2, comprising:
S21. the spacecraft is obtained in the end point velocity inertial V of end of braking point position0In local horizontal component VxAnd diameter To component Vy；
S22. according to the horizontal component VxWith the radial component VyObtain the end point velocity inertial V0And it is described used Property speed V0Velocity inertial inclination angle theta0；
S23. according to the end point velocity inertial V0With the velocity inertial inclination angle theta0The spacecraft is obtained in the cunning of coasting-flight phase Row section voyage angle
S24. according to the coasting-flight phase voyage Sb2, the braking duration tpWith coasting-flight phase voyage angleDescribed second is established to close It is formula；
S25. according to second relational expression, second gradient is calculated using chain type Rule for derivation.
4. calculation method according to claim 3, which is characterized in that in step S21, it is assumed that retro-speed increment is arteries and veins Punching, position is at the midpoint of the retaining segment, then horizontal component VxAre as follows:
Radial component VyAre as follows:
Wherein, Vi0For the brake inertia speed of braking point, θiFor the speed inclination angle of braking point velocity inertial, Δ ν is retro-speed Increment, ψzFor braking pitch angle and-π≤ψz< π.
5. calculation method according to claim 4, which is characterized in that in step S23, coasting-flight phase voyage angleAre as follows:
Coefficient in expression formula are as follows:
A=2Re(1+tan2θ0)-(Rd0+Re)ν0,
B=Reν0tanθ0,
C=(Rd0-Re)ν0,
Wherein, μ is Gravitational coefficient of the Earth, ReFor the geocentric distance of reentry point.
6. calculation method according to claim 5, which is characterized in that in step S25, comprising:
S251 calculates coasting-flight phase voyage anglePartial derivative and second relationship to coefficient in second relational expression Coefficient is to the end point velocity inertial V in formula0With the velocity inertial inclination angle theta0Partial derivative；
S252. the end point velocity inertial V is calculated separately0With the velocity inertial inclination angle theta0To the end point velocity inertial V0In local horizontal component VxWith radial component VyPartial derivative；
S253. the end point velocity inertial V is calculated0In local horizontal component VxWith radial component VyTo the retro-speed The partial derivative of increment Delta ν and the retro-speed increment Delta ν are to the braking duration tpPartial derivative.
7. calculation method according to claim 6, which is characterized in that in step S3, comprising:
S31. the retaining segment voyage angle δ of the spacecraft retaining segment is obtainedb, the orbital eccentricity e of the spacecraft coasting-flight phase, with And the orbital angular momentum h of coasting-flight phase；
S32. according to retaining segment voyage angle δb, the orbital eccentricity e, the orbital angular momentum h and the coasting-flight phase voyage Angle ψbObtain the reentry angle θ of spacecrafte；
S33. according to the reentry stage voyage Sb3, the braking duration tp, the reentry angle θeWith spacecraft parachute-opening point speed Inclination angle thetafEstablish the third relational expression；
S34. according to the third relational expression, the 3rd gradient is calculated using chain type Rule for derivation.
8. calculation method according to claim 7, which is characterized in that in step S32, retaining segment voyage angle δbAre as follows:
The orbital eccentricity e are as follows:
The orbital angular momentum h are as follows:
H=Rd0V0cosθ0,
The reentry angle θeAre as follows:
9. calculation method according to claim 8, which is characterized in that in step S34, comprising:
S341. retaining segment voyage angle δ is calculatedbTo the braking duration tpPartial derivative；
S342. the orbital eccentricity e and the orbital angular momentum h are calculated to the end point velocity inertial V0With the inertia Speed inclination angle theta0Partial derivative；
S343. reentry angle θ is calculatedeTo the orbital eccentricity e, retaining segment voyage angle δb, coasting-flight phase voyage angle ψb、 The partial derivative of the orbital angular momentum h；
S344. the reentry stage voyage S is calculatedb3To the reentry angle θeWith the parachute-opening spot speed inclination angle thetafPartial derivative；
S345. the parachute-opening spot speed inclination angle theta is calculatedfTo the reentry angle θePartial derivative.
10. calculation method according to claim 9, which is characterized in that in step S344, construct the reentry stage voyage Sb3 With the reentry angle θeWith the parachute-opening spot speed inclination angle thetafThe 4th relational expression, based on the 4th relational expression calculate it is described again Enter a section voyage Sb3To the reentry angle θeWith the parachute-opening spot speed inclination angle thetafPartial derivative；
4th relational expression are as follows:
Wherein, β is atmospheric density ρ to the gradient of height H and the ratio of atmospheric density, i.e.,
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