 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Ya.G. Sapunkov and Yu.N. Chelnokov, "Pulsed Optimal Reorientation of the Orbit of a Spacecraft by Means of Reactive Thrust Orthogonal to the Osculating Orbit. I," Mech. Solids. 53 (5), 535-551 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
5 |
Pages |
535-551 |
| DOI |
10.3103/S0025654418080083 |
| Title |
Pulsed Optimal Reorientation of the Orbit of a Spacecraft by Means of Reactive Thrust Orthogonal to the Osculating Orbit. I |
| Author(s) |
Ya.G. Sapunkov (Institute of Precision Mechanics and Control Problems of the Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia)
Yu.N. Chelnokov (Institute of Precision Mechanics and Control Problems of the Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia; Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia, ChelnokovYuN@gmail.com) |
| Abstract |
The first part of the article provides an overview of the work on the differential equations of the orbit orientation of a spacecraft (SC) and the problem of optimal reorientation of a spacecraft's orbit in an inertial coordinate system by means of reactive acceleration orthogonal to the osculating plane of the spacecraft. The theory of solving the problem of the optimal reorientation of the orbit of the spacecraft using the quaternionic differential equation for the orientation of the orbital coordinate system in a non-linear continuous formulation (using limited (small) thrust) is presented. As a minimized quality functional, a combined functional is used equal to the weighted sum of the reorientation time and thrust impulse (characteristic speed) during the reorientation of the orbit of the spacecraft (special cases of this functional are the speed response case and the characteristic speed minimization separately).
The theory outlined in the first part of the article is used in the second part of the article to build in a strict non-linear formulation of the new theory and new algorithms for numerical solution of the problem of the optimal reorientation of the spacecraft orbit in the inertial coordinate system by means of pulsed (high) thrust, orthogonal to the plane of an osculating orbit, using the quaternionic differential equation for the orientation of the orbital coordinate system for an unfixed number of pulses of reactive thrust. The constructed algorithms allow for the numerical solution of the problem to determine the optimal moments of switching on a reactive engine, the optimal values of reactive acceleration pulses and their optimal number. Examples are given of a numerical solution of the problem of optimal impulse reorientation of the orbit of the spacecraft, demonstrating the capabilities of the proposed method. |
| Keywords |
spacecraft orbit, optimal orbit reorientation, reactive acceleration, orthogonal to the orbit plane, quaternion |
| References |
| 1. | G.N. Duboshin,
Celestial Mechanics: Basic Problems and Methods
(Nauka, Moscow, 1968) [in Russian]. |
| 2. | V.K. Abalakin, E.P. Aksenov, E.A. Grebenikov, et al.,
Reference Manual in Celestial Mechanics and Astrodynamics
(Nauka, Moscow, 1976) [in Russian]. |
| 3. | Yu.M. Kopnin,
"On the Task of Rotating a Satellite's Orbit Plane,"
Kosm. Issl.
3 (4) (1965). |
| 4. | V.N. Lebedev,
Calculation of Motion of a Spacecraft with Low Thrust
(VZ AN, Moscow, 1968) [in Russian]. |
| 5. | M.Z. Borshchevskii and M.V. Ioslovich,
"On the Problem of Rotating the Orbital Plane of a Satellite by Means of Reactive Thrust,"
Kosm. Issl.
7 (6) (1969). |
| 6. | G.L. Grodzovskii, Yu.N. Ivanov, and V.V. Tokarev,
Mechanics of Space Flight, Optimization Problems
(Nauka, Moscow, 1975) [in Russian]. |
| 7. | D.E Okhotsimskii and Yu.G. Sikharulidze,
Foundations of Space Flight Mechanics (Nauka, Moscow, 1990) [in Russian]. |
| 8. | S.A. Ishkov and V.A. Romanenko,
"Forming and Correction of a High-Elliptical Orbit of an Earth Satellite with Low-Thrust Engine,"
Kosm. Issl.
35 (3), 11-20 (1997)
[Cosm. Res. (Engl. Transl.)
35 (3), 268-277 (1997)]. |
| 9. | Yu.N. Chelnokov,
"Application of Quaternions in the Theory of Orbital Motion of an Artificial Satellites. II,"
Kosm. Issl.
31 (3), 3-15 (1993)
[Cosm. Res. (Engl. Transl.)
31 (3), 409-418 (1993)]. |
| 10. | Yu.N. Chelnokov,
Quaternion and Biquaternion Models and Methods of Mechanics of Solids and Their Applications
(Fizmatlit, Moscow, 2006) [in Russian]. |
| 11. | Yu.N. Chelnokov,
Quaternion Models and Methods of Dynamics, Navigation, and Control of Motion
(Fizmatlit, Moscow, 2011) [in Russian]. |
| 12. | Yu.N. Chelnokov,
"Optimal Reorientation of a Spacecrafts Orbit Using a Jet Thrust Orthogonal to the Orbital Plane,"
Prikl. Mat. Mekh.
76 (6), 895-912 (2012)
[J. App. Mat. Mech. (Engl. Transl.)
76 (6), 646-657 (2012)]. |
| 13. | Yu.N. Chelnokov,
"Quaternion Regularization and Trajectory Motion Control in Celestial Mechanics and Astrodynamics: II,"
Kosm. Issl.
52 (4), 322-336 (2014)
[Cosm. Res. (Engl. Transl.)
52 (4), 314-317 (2014)]. |
| 14. | S.V. Nenakhov and Yu.N. Chelnokov,
"Quaternion Solution of the Problem of Optimal Control of Orientation of the Orbit of a Spacecraft,"
in Proceedings of the International Conference Onboard Integrated Complexes and Modern Control Problems
(Izdat. MAI, Moscow, 1998), pp. 59-60 [in Russian]. |
| 15. | D.A. Sergeev and Yu.N. Chelnokov,
"Optimum control of spacecraft orbit orientation,"
in Mathematics. Mechanics
(Izdat. Saratov Univ., Saratov, 2001), Vol. 3, pp. 185-188 [in Russian]. |
| 16. | D.A. Sergeev and Yu.N. Chelnokov,
"Optimal Control of Spacecraft's Orbit's Orientation,"
in Problems of Precise Mechanics and Control, Collection of Papers
(Izdat. Saratov Univ., Saratov, 2002), pp. 64-75 [in Russian]. |
| 17. | I.A. Pankratov, Ya.G. Sapunkov, and Yu.N. Chelnokov,
"About a Problem of Spacecraft’s Orbit Optimal Reorientation,"
Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
12 (3), 87-95 (2012). |
| 18. | Yu.N. Chelnokov,
"Application of Quaternions in Theory of Orbital Motion of Artificial Satellite. I,"
Kosm. Issl. 30 (6), 759-770 (1992)
[Cosm. Res. (Engl. Transl.) 30 (6), 612-621 (1992)]. |
| 19. | Yu.N. Chelnokov,
"Construction of Optimum Controls and Trajectories of Spacecraft Flight by Employing Quaternion Description of Orbit Spatial Orientation,"
Kosmich. Issled.
534-542 (1997)
[Cosmic Res. (Engl. Transl.)
35 (5), 499-507 (1997)]. |
| 20. | V.N. Branets and I.P. Shmyglevskii,
Application of Quaternions in Problems of Attitude Control of a Rigid Body
(Nauka, Moscow, 1973) [in Russian]. |
| 21. | A.F. Bragazin, V.N. Branets, and I.P. Shmyglevskii,
"Description of Orbital Motion Using Quaternions and Velocity Parameters,"
in Abstracts of Reports at the 6th All-Union Congress on Theoret. and Applied Mechanics, (Fan, Tashkent, 1986), p. 133 [in Russian]. |
| 22. | V.N. Branets and I.P. Shmyglevskii,
Introduction to the Theory of Strapdown Inertial Navigation Systems
(Nauka, Moscow, 1992) [in Russian]. |
| 23. | Yu.N. Chelnokov,
"Optimal Reorientation of Spacecraft’s Orbit through Thrust
Orthogonal to the Plane of Orbit,"
in Mathematics, Mechanics, Collection of Papers, No. 8 (Izdat. Saratov Univ., Saratov, 2006), pp. 231-234 [in Russian]. |
| 24. | Yu.N. Chelnokov,
"Optimum Reorientation of the Spacecraft Orbit: Quaternion Approach to Problem Solution,"
in Proc. of Intern. Conf. on Problems and Prospects of Precision Mechanics and Control in the Mechanical Engineering
(Izd. STGU, Saratov, 2006), pp. 54-60 [in Russian]. |
| 25. | I.A. Pankratov, Ya.G. Sapunkov, and Yu.N. Chelnokov,
"Solution of a Problem of Spacecraft’s Orbit OptimalReorientation Using Quaternion Equations of Orbital Systemof Coordinates Orientation,"
Izv. Saratov Univ. (N. S.) Ser. Math. Mekh. Inform.
13 (1), 84-92 (2013). |
| 26. | V.A. Il'in and G.E. Kuzmak,
Optimal Flights of Spacecraft
(Nauka, Moscow, 1976) [in Russian]. |
| 27. | Yu.N. Chelnokov,
"Analysis of Optimal Motion Control for a Material Point in a Central Field with Application of Quaternions,"
Izv. Akad. Nauk. Teor. Sist. Upr.
No. 5, 18-44 (2007)
[J. Comp. Sys. Sci. Int. (Engl. Transl.)
46 (5) 688-713 (2007)]. |
| 28. | Yu.V. Afanas'eva and Yu.N. Chelnokov,
"The Problem of Optimal Control of the Orientation of an Orbit of a Spacecraft as a Deformable Figure,"
Izv. Akad. Nauk. Teor. Sist. Upr.
No. 4, 125-138 (2008)
[J. Comp. Sys. Sci. Int. (Engl. Transl.)
47 (4) 621-634 (2008)]. |
| 29. | Yu.V. Afanas'eva and Yu.N. Chelnokov,
"The Problem of Rendezvous of a Controlled Space Vehicle with an Uncontrolled Space Vehicle Moving Along an Elliptical Keplerian Orbit in the Central Newtonian Gravitational Field,"
Izv. Akad. Nauk. Teor. Sist. Upr.
No. 3, 164-179 (2007)
[J. Comp. Sys. Sci. Int. (Engl. Transl.)
46 (3) 468-483 (2007)]. |
| 30. | Yu.N. Chelnokov,
"On Estimating the Orientation of an Object in Rodrigues-Hamilton Parameters Using its Angular Velocity,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 11-20 (1977). |
|
| Received |
09 February 2016 |
| Link to Fulltext |
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