CN105373167B - Electronic rope system spacecraft Asymptotic Stability releasing control method - Google Patents
Electronic rope system spacecraft Asymptotic Stability releasing control method Download PDFInfo
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- CN105373167B CN105373167B CN201510509206.1A CN201510509206A CN105373167B CN 105373167 B CN105373167 B CN 105373167B CN 201510509206 A CN201510509206 A CN 201510509206A CN 105373167 B CN105373167 B CN 105373167B
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Abstract
The invention provides a kind of electronic rope system spacecraft Asymptotic Stability releasing control method.Under the line under circular orbit, the technology is primarily based on the expectation angle of pitch that electric power setting meets value requirement, realizes that the Asymptotic Stability of electric rope discharges process further according to the rope release dimensionaless speed control proposed.The present invention solve how to make electronic rope under the line under circular orbit Asymptotic Stability along it is expected angle of pitch release, according to the electric rope rate of release calculated with can realizing space rope system spacecraft Asymptotic Stability releasing control method；Meanwhile it can also realize that rope at the uniform velocity discharges by adjusting current strength.
Description
Technical field
The present invention relates to Spacecraft Control field, specifically a kind of electronic rope system spacecraft Asymptotic Stability release control side
Method.
Background technology
During the release of space tethered system, latter stage in stage is especially discharged, rope is easily produced and significantly swung.This
Outside, when performing the space tasks such as space junk removal, orbital acquisition, radiation zone reparation, all need to be discharged by in-orbit spacecraft
Task could be completed by going out an end and being connected to the electric rope of detector, and bibliography is as follows
Barkow B,Steindl A,Troger H.A targeting strategy for the deployment
of a tethered satellite system.IMA Journal of Applied Mathematics,2005,70(5):
626-644.
Williams J D,Sanmartin J R,Rand L P.Low work-function coating for an
entirely propellantless bare electrodynamic tether.IEEE Transactions on
Plasma Science,2012,40(5):1441-1445.
Schadegg M M,Russell R P,Lantoine G.Jovian orbit capture and
eccentricity reduction using electrodynamic tether propulsion.Journal of
Spacecraft and Rockets,2015,52(2):506-516.
Electronic rope system spacecraft is generally by in-orbit spacecraft, end detector and the electric rope three parts group for connecting both ends
Into.Wherein, the electronic rope with conductive characteristic can cut ground magnetic induction line when orbiting the earth, and it is electronic to produce powerful dynamic life
Gesture, while electric charge collection and emitter are installed to produce electric current, electric current meeting and earth magnetism when by tether in tether end
Field interactions and produce electric power.It is, in general, that electrodynamic action can all make space rope system system become unstable, and cause
There is complicated dynamic behavior, it is necessary to which extra control device could be restrained, bibliography is as follows
Zhong R,Zhu Z H.Long term dynamics and optimal control of nano-
satellite deorbit using a short electrodynamic tether.Advances in Space
Research,2013,52(8):1530-1544.
M,Lanchares V,Pascual A I et al.Attitude stabilization of
electrodynamic tethers in elliptic orbits by time-delay feedback control.Acta
Astronautica,2014,96(1):280-295.
Sánchez-Arriaga G,Bombardelli C,Chen X.Impact of nonideal effects on
bare electrodynamic tether performance.Journal of Propulsion and Power,2015,
31(3):951-955.
Some release controls having pointed out at present are all built upon the control strategy on the basis of non-electrical power, such as only by releasing
The rope release of the progress such as speed, pulling force regulation, optimum control is put, bibliography is as follows
Jin D P,Hu H Y.Optimal control of a tethered subsatellite of three
degrees of freedom.Nonlinear Dynamics,2006,46(1-2):161-178.
The tethered satellite time optimal release control mechanics journals that Wen Hao, Jin Dongping, Hu Haiyan are included based on differential,
2008,40(1):135-140.
Liu Y Y,Zhou J,Chen H L.Variable structure control for tethered
satellite fast deployment and retrieval.Future Control and Automation,2012,
172(1):157-164.
The content of the invention
The present invention in order to solve how to make electronic rope under the line under circular orbit Asymptotic Stability along it is expected angle of pitch release
A kind of problem, there is provided electronic rope system spacecraft Asymptotic Stability releasing control method, it is possible to achieve electronic rope system spacecraft is red
Asymptotic Stability release under road circular orbit, effectively suppress to swing in the face of rope and outside face.Meanwhile by adjusting current strength also
It can realize that rope at the uniform velocity discharges.
The present invention comprises the following steps：
Step A, the system angle of pitch, the dimensionless dynamics side of rolling angular oscillatory motion during the release of structure description electric rope
Journey
In formula, θ represents the angle of pitch in the face of electric rope swing,The angle of pitch is asked track true anomaly ν in expression face
Lead, i.e., rate of pitch in the face of rope swing,The second dervative of the angle of pitch in the face of rope swing is represented, φ represents electronic
Roll angle outside the face of rope swing,The outer roll angle in expression face rolls to track true anomaly ν derivations that is, outside the face of rope swing
Tarnsition velocity,The second dervative of roll angle outside the face of rope swing is represented, ξ represents rope non-dimensional length,Represent rope
The rate of change of non-dimensional length, parameter Hθ=-[μmI(mM-mS)cosδ]/[2μEmMmS]、Hφ=0, wherein μmRepresent that the earth is even
Extremely sub- magnetic moment, I represent rope current strength, mMRepresent spacecraft mass, mSEnd detector quality is represented, δ represents that track inclines
Angle, μERepresent Gravitational coefficient of the Earth.Obviously, the parameter H if current IconstθAlso it is steady state value.
Step B, the equalization point of system is determined according to formula (1)
In formula, θ10For the equilbrium position angle of pitch, θ20For corresponding rate of pitch, φ10For equilbrium position roll angle, φ20
For corresponding angular velocity in roll, due to Hφ=0 event equilbrium position roll angle φ10=0.
Step C, it is any that an expectation pitching angle theta is sete, and make equilbrium position pitching angle theta10=θe, determine θeWith parameter
Hθ, rope non-dimensional length ξ and its rate of changeRelation, it is as follows
Step D, determine it is expected pitching angle theta according to the characteristic root of system linearization matrix and release characteristicseSpan,
So that when being discharged to electric rope, ensure rope release process Asymptotic Stability；
Step E, pitching angle theta it is expectedeUnder conditions of meeting span, released according to the dimensionless that formula (3) rope discharges
Put speed and release control is carried out to electric rope.
Further improve, in the stable release control technology of space device rope of the present invention, it is expected in the step D
Pitching angle thetaeSpan, it is as follows
When rope discharges, as long as the expectation angle of pitch of setting meetsRope can enter in circular orbit
Discharge row Asymptotic Stability.
Meanwhile the at the uniform velocity release that electric power realizes rope can be changed by adjusting current strength, it is as follows
When rope discharges, as long as current strength is controlled by above formula, the stable at the uniform velocity release of rope can be realized.In addition,
It is noted that by formula (4) can draw formula (7) be it is permanent set up, so when it is expected pitching angle thetaeSelection be arbitrary.
Beneficial effect of the present invention is：
(1) technology can realize Asymptotic Stability release of the electronic rope system spacecraft under the line under circular orbit, effectively suppress
Swung in the face of rope and outside face；
(2) technology can make end detector carry out stablizing release with the expectation angle of pitch of arbitrary size；
(3) by adjusting electric current in real time, it is possible to achieve the stable at the uniform velocity release of electric rope.
Brief description of the drawings
Fig. 1 is that the electronic rope system spacecraft of patent of the present invention description discharges system schematic；
Fig. 2 (a) is angle of pitch change schematic diagram in electric rope face during Asymptotic Stability release control；
Fig. 2 (b) is roll angle change schematic diagram outside electric rope face during Asymptotic Stability release control；
Fig. 2 (c) is track schematic diagram of the electronic rope system detector under Asymptotic Stability release control；
Fig. 2 (d) is dimensionless rope lengths change schematic diagram under electronic rope system Asymptotic Stability release control；
Fig. 3 (a) is angle of pitch change schematic diagram in electric rope face during Asymptotic Stability at the uniform velocity release control；
Fig. 3 (b) is roll angle change schematic diagram outside electric rope face during Asymptotic Stability at the uniform velocity release control；
Fig. 3 (c) is track schematic diagram of the electronic rope system detector under Asymptotic Stability at the uniform velocity release control；
Fig. 3 (d) is the change schematic diagram of control electric current during Asymptotic Stability at the uniform velocity discharges.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
A kind of specific electronic rope system spacecraft release system as shown in figure 1, in electronic rope system spacecraft release system,
Including roll angle 2, spacecraft 3, detector 4, conductive rope 5, true anomaly ν 6, the earth 7, equator outside pitching angle theta in face 1, face
Plane 8, orbit plane 9, ascending node 10, orbit inclination angle 11, the angle of pitch 1 is by projection of the rope in orbit plane and ground wherein in face
The heart and spacecraft centroid line are formed, and roll angle 2 is made up of rope and orbit plane angle outside face.
The present invention is a kind of stable release control technology of space electric rope system spacecraft, under the line under circular orbit, i.e. track
Inclination angle 11 is taken as 0, and the technology is primarily based on the expectation angle of pitch that electric power setting meets value requirement, further according to the rope proposed
The stable release process of electric rope is realized in rope release dimensionaless speed control, specifically includes following steps：
Step A, the system angle of pitch, the dimensionless dynamics side of rolling angular oscillatory motion during the release of structure description electric rope
Journey
In formula, θ represents the angle of pitch in the face of electric rope swing,The angle of pitch is asked track true anomaly ν in expression face
Lead, i.e., rate of pitch in the face of rope swing,The second dervative of the angle of pitch in the face of rope swing is represented, φ represents electronic
Roll angle outside the face of rope swing,The outer roll angle in expression face is to track true anomaly ν derivations, i.e. rolling outside the face of rope swing
Angular speed,The second dervative of roll angle outside the face of rope swing is represented, ξ represents rope non-dimensional length,Represent rope without
The rate of change of dimension length, parameter Hθ=-[μmI(mM-mS)cosδ]/[2μEmMmS]、Hφ=0, wherein μmRepresent earth dipole
Sub- magnetic moment, I represent rope current strength, mMRepresent spacecraft mass, mSEnd detector quality is represented, δ represents orbit inclination angle,
μERepresent Gravitational coefficient of the Earth.Obviously, the parameter H if current IconstθAlso it is steady state value.
Step B, θ is made1=θ,φ1=φ,System balancing point can determine that according to formula (1).By formula (1)
It is written as normal form
According to this normal form, system balancing point is easily obtained
In formula, θ10For the equilbrium position angle of pitch, θ20For corresponding rate of pitch, φ10For equilbrium position roll angle, φ20
For corresponding angular velocity in roll, due to Hφ=0 event equilbrium position roll angle φ10=0.
Step C, it is any that an expectation pitching angle theta is sete, and make equilbrium position pitching angle theta10=θe, determine θeWith parameter
Hθ, rope non-dimensional length ξ and its rate of changeRelation, it is as follows
Step D, determine it is expected pitching angle theta according to the characteristic root of system linearization matrix and release characteristicseSpan,
So that when being discharged to electric rope, ensure rope release process Asymptotic Stability.
According to the linearisation matrix of normal form (2)
Its characteristic root can be written
Make characteristic root real part be less than zero, and formula (4) substitution can wherein be obtained
Meanwhile when being discharged for rope, haveAlso can obtain and above formula identical result
It is expected pitching angle theta in the step DeSpan, as formula (7).Therefore, when rope discharges, as long as setting
The fixed expectation angle of pitch meetsRope can discharge while Asymptotic Stability is carried out in circular orbit.
Step E, pitching angle theta it is expectedeUnder conditions of meeting span, released according to the dimensionless that formula (4) rope discharges
Put speed and release control is carried out to electric rope.
In addition, give a dimensionless rate of releaseBy it and parameter Hθ=-[μmI(mM-mS)]/[2μEmMmS] together
In substitution formula (4), current control rule can be obtained, it is as follows
When rope discharges, as long as current strength is controlled by above formula, the stable at the uniform velocity release of rope can be realized.In addition,
By formula (4) can draw formula (7) be it is permanent set up, so when it is expected pitching angle thetaeSelection be arbitrary.
The electronic rope system release process of one group of parameters on space spacecraft is taken to carry out numerical simulation.If spacecraft and end are visited
The quality for surveying device is respectively 500kg and 20kg, the initial true anomaly ν of system0=0, orbit inclination angle is δ=0；Initial time,
Dimensionless rope lengths ξ0=0.05, perturb pitching angle theta0=-0.02rad and angular speedPerturb roll angle
φ0=-0.1rad and angular speedCurrent strength is I=-1A.According to the asymptotically stable released strip of electronic rope
Part, it can calculate and it is expected that angle of pitch span is θe＜ 0.16rad, therefore expectation pitching angle theta might as well be takene=0.05rad.
Shown in embodiment Numerical Simulation Results such as Fig. 2 (a), Fig. 2 (b), Fig. 2 (c) and Fig. 2 (d).Fig. 2 (a) expression systems are bowed
The elevation angle with true anomaly ν situation of change, rope by around it is expected angle swing repeatedly after, will gradually level off to it is expected pitching
Angle 0.05rad.Fig. 2 (b) represents situation of change of the system roll angle with true anomaly ν, and rope will gradually become after swinging repeatedly
It is bordering on roll angle equilbrium position 0.Fig. 2 (c) illustrates under orbital coordinate system o- χ η that (i.e. origin o is consolidated in spacecraft centroid, χ axles
Spacecraft motion opposite direction is pointed to, η axles point to spacecraft centroid by earth centroid) the release track of electric rope.As can be seen that
The rope release control proposed according to this patent is restrained, even if system has initial pitch angle perturbation and roll angle perturbation, rope
Also will be along expectation pitching angle thetaeRelease, that is, it is asymptotically stable to discharge process.Here, electric power does not make system unstability,
But the span for it is expected angle of pitch is expanded, and enable electric rope is asymptotically stable to discharge.Therefore, this patent is carried
The control law gone out discharges process with can realizing electric rope Asymptotic Stability.Fig. 2 (d) be electronic rope system dimensionless rope lengths with
True anomaly ν situation of change.
WithThe embodiment Numerical Simulation Results at the uniform velocity discharged are as shown in Figure 3.Fig. 3 (a) represents the system angle of pitch
With true anomaly ν situation of change, rope it is expected the angle of pitch after around the swing repeatedly for it is expected angle, by gradually leveling off to
0.05rad.Fig. 3 (b) represents situation of change of the system roll angle with true anomaly ν, after swinging repeatedly, gradually will level off to rolling
Corner equilbrium position 0.Fig. 3 (c) illustrates the release track of the electric rope under orbital coordinate system o- χ η.As can be seen that basis
The rope that this patent is proposed at the uniform velocity release control is restrained, even if initial pitch angle perturbation and roll angle perturbation be present, rope also may be used
Pitching angle theta it is expected with edgeeDischarge Asymptotic Stability.Therefore, the control law that this patent is proposed can also realize electric rope
Asymptotic Stability at the uniform velocity discharges.Fig. 3 (d) illustrates the situation of change of control electric current during at the uniform velocity release.
Concrete application approach of the present invention is a lot, and described above is only the preferred embodiment of the present invention, it is noted that for
For those skilled in the art, under the premise without departing from the principles of the invention, some improvement can also be made, this
A little improve also should be regarded as protection scope of the present invention.
Claims (3)
1. a kind of electronic rope system spacecraft Asymptotic Stability releasing control method, it is characterised in that comprise the following steps：
Step A, the system angle of pitch, the dimensionless kinetics equation of rolling angular oscillatory motion during the release of structure description electric rope：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mfrac>
<mover>
<mi>&xi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>&xi;</mi>
</mfrac>
<mo>-</mo>
<mi>&phi;</mi>
<mover>
<mi>&phi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mi>&theta;</mi>
<mo>=</mo>
<msub>
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<mi>&theta;</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>&phi;</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mo>+</mo>
<mn>2</mn>
<mover>
<mi>&phi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&xi;</mi>
<mi>&xi;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mo>&lsqb;</mo>
<msup>
<mrow>
<mo>(</mo>
<mover>
<mi>&theta;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>3</mn>
<mo>&rsqb;</mo>
<mi>&phi;</mi>
<mo>=</mo>
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<mi>&phi;</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
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<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, θ represents the angle of pitch in the face of electric rope swing,The angle of pitch is to track true anomaly ν derivations in expression face, i.e.,
Rate of pitch in the face that electric rope is swung,The second dervative of the angle of pitch in the face that electric rope is swung is represented, φ is represented
Roll angle outside the face that electric rope is swung,The outer roll angle in expression face is swung to track true anomaly ν derivations, i.e. electric rope
Angular velocity in roll outside face,The second dervative of roll angle outside the face that electric rope is swung is represented, ξ represents electric rope dimensionless length
Degree,Represent the rate of change of electric rope non-dimensional length, parameter Hθ=-[μmI(mM-mS)cosδ]/[2μEmMmS]、Hφ=0,
Wherein μmGeomagnetic dipole magnetic moment is represented, I represents electric rope current strength, mMRepresent spacecraft mass, mSRepresent distal probe
Device quality, δ represent orbit inclination angle, μERepresent Gravitational coefficient of the Earth, the parameter H if current IconstθAlso it is steady state value；
Step B, the equalization point of system is determined according to formula (1)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>10</mn>
</msub>
<mo>=</mo>
<mfrac>
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<msub>
<mi>&xi;H</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mn>2</mn>
<mover>
<mi>&xi;</mi>
<mo>&CenterDot;</mo>
</mover>
</mrow>
<mrow>
<mn>3</mn>
<mi>&xi;</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mn>20</mn>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&phi;</mi>
<mn>10</mn>
</msub>
<mo>=</mo>
<mo>-</mo>
<mfrac>
<msub>
<mi>H</mi>
<mi>&phi;</mi>
</msub>
<mn>4</mn>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&phi;</mi>
<mn>20</mn>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, θ10For the equilbrium position angle of pitch, θ20For corresponding rate of pitch, φ10For equilbrium position roll angle, φ20To be right
The angular velocity in roll answered, due to Hφ=0 event equilbrium position roll angle φ10=0；
Step C, it is any that an expectation pitching angle theta is sete, and make equilbrium position pitching angle theta10=θe, determine θeWith parameter Hθ, electricity
Running rope rope non-dimensional length ξ and its rate of changeRelation, it is as follows
<mrow>
<mover>
<mi>&xi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&xi;H</mi>
<mi>&theta;</mi>
</msub>
<mo>-</mo>
<mn>3</mn>
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<mi>&xi;&theta;</mi>
<mi>e</mi>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
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<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Step D, determine it is expected pitching angle theta according to the characteristic root of system linearization matrix and release characteristicseSpan so that
When being discharged to electric rope, ensure electric rope release process Asymptotic Stability；
Step E, pitching angle theta it is expectedeUnder conditions of meeting span, speed is changed according to formula (4) electric rope non-dimensional length
RateRelease control is carried out to electric rope.
2. electronic rope system spacecraft Asymptotic Stability releasing control method according to claim 1, it is characterised in that：The step
It is expected pitching angle theta in rapid DeSpan it is as follows：
<mrow>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo><</mo>
<mfrac>
<msub>
<mi>H</mi>
<mi>&theta;</mi>
</msub>
<mn>3</mn>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
3. electronic rope system spacecraft Asymptotic Stability releasing control method according to claim 1, it is characterised in that：Step E
In to electric rope carry out release control when, give a dimensionless rate of releaseCurrent control rule is as follows：
<mrow>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>&xi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
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<msub>
<mi>&mu;</mi>
<mi>E</mi>
</msub>
<msub>
<mi>m</mi>
<mi>M</mi>
</msub>
<msub>
<mi>m</mi>
<mi>S</mi>
</msub>
<mo>&lsqb;</mo>
<mn>2</mn>
<msub>
<mover>
<mi>&xi;</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>e</mi>
</msub>
<mo>+</mo>
<mn>3</mn>
<msub>
<mi>&xi;&theta;</mi>
<mi>e</mi>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>m</mi>
<mi>M</mi>
</msub>
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<msub>
<mi>m</mi>
<mi>S</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
When electric rope discharges, as long as current strength is controlled by above formula, the stable at the uniform velocity release of electric rope can be realized, this
When it is expected the angle of pitch be θe。
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| CN106054906B (en) * | 2016-05-30 | 2019-04-19 | 南京航空航天大学 | Drive lacking releasing control method based on non-linear space rope system system |
| CN106516177B (en) * | 2016-10-18 | 2019-07-19 | 南京航空航天大学 | It is a kind of based on rope be technology space junk recycling and control method |
| CN112520066B (en) * | 2020-11-25 | 2022-06-28 | 中山大学 | Full-electric stable control method for large-orbit eccentricity multi-body tethered satellite |
| CN113311863B (en) * | 2021-05-25 | 2022-07-08 | 南京航空航天大学 | Method for judging dynamic behavior stability of space linear type rope system observation system |
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