Spacecraft with Periodic Mass Redistribution:

A. A. Burov ; I. I. Kosenko ; V. I. Nikonov

Russian journal of nonlinear dynamics, Tome 18 (2022) no. 4, pp. 639-649.

Résumé

The motion of a spacecraft containing a moving massive point in the central field of Newtonian attraction is considered. Within the framework of the so-called “satellite approximation”, the center of mass of the system is assumed to move in an unperturbed elliptical Keplerian orbit. The spacecraft’s dynamics about its center of mass is studied. Conditions under which the spacecraft rotates about a perpendicular to the plane of the orbit uniformly with respect to the true anomaly are found. Such uniform rotations are achieved using a specially selected rule for changing the position of a massive point with respect to the spacecraft. Necessary conditions for these uniform rotations are studied numerically. An analysis of the nonintegrability of a special class of spacecraft’s rotation is carried out using the method of separatrix splitting. Poincaré sections are constructed for certain parameter values. Several linearly stable periodic motions are pointed out and investigated.

Détail

Keywords: spacecraft attitude dynamics, spacecraft in an elliptic orbit, spacecraft with variable mass distribution, spacecraft’s chaotic oscillations, spacecraft’s periodic motions.

Bibliographie

[1] Roberson, R. E., “Torques on a Satellite Vehicle from Internal Moving Parts”, J. Appl. Mech., 25:2 (1958), 196–200

[2] Roberson, R. E., “Torques on a Satellite Vehicle from Internal Moving Parts (Supplement)”, J. Appl. Mech., 25:2 (1958), 287–288

[3] Haeussermann, W., “An Attitude Control System for Space Vehicles”, J. ARS, 29:3 (1959), 203–207

[4] Merrick, V. K., Some Control Problems Associated with Earth-Oriented Satellites, NASA Technical Note D-1771, Natl. Aeronaut. Space Admin., Washington, D.C., 1963, 80 pp.

[5] Roberson, R. E., “Comments on the Incorporation of Man into the Attitude Dynamics of Spacecraft”, J. Astronaut. Sci., 10:1 (1963), 27–28

[6] Thomson, W. T. and Fung, Y. C., “Instability of Spinning Space Stations due to Crew Motion”, AIAA Journal, 3:6 (1965), 1082–1087

[7] Harding, C. F., “Manned Vehicles As Solids with Translating Particles: 1”, J. Spacecraft Rockets, 2:3 (1965), 465–467

[8] Schiehlen, W., Über die Lagestabilisirung künstlicher Satelliten auf elliptischen Bahnen, Doctoral Dissertation, Technische Hochschule Stuttgart, Stuttgart, 1966, 148 pp.

[9] Schiehlen, W., “Über den Drallsatz für Satelliten mit im Innern bewegten Massen”, Z. Angew. Math. Mech., 46 (1966), T132–T134

[10] Schiehlen, W. and Kolbe, O., “Gravitationsstabilisierung von Satelliten auf elliptischen Bahnen”, Ing. Arch., 38:6 (1969), 389–399

[11] Poli, C. R., “Effect of Man's Motion on the Attitude of a Satellite”, J. Spacecraft Rockets, 4:1 (1967), 15–20

[12] Edwards, T. L., A Movable Mass Control System to Detumble a Disabled Space Vehicle, Astronautics Research Report No. 73-5, Pensylvania State University, University Park, Penn., 1973, 91 pp.

[13] Kunciw, B. G. and Kaplan, M. H., “Optimal Space Station Detumbling by Internal Mass Motion”, Automatica, 12:5 (1976), 417–425

[14] Bainum, P. M. and Sellappan, R., The Dynamics of Spin Stabilized Spacecraft with Movable Appendages: Part 2, Final Report NASA-CR-148815, Howard University, Washington, D.C., 1976, xi, 110 pp.

[15] Bainum, P. M. and Sellappan, R., “The Use of a Movable Telescoping End Mass System for the Time-Optimal Control of Spinning Spacecraft”, Acta Astronaut., 5:10 (1978), 781–795

[16] Polyanskaya, I. P., “Oscillations of a Satellite with Compensating Devices in an Elliptical Orbit”, Kosmicheskie Issledovaniya, 20:5 (1982), 674–681 (Russian)

[17] Rochon, B. V. and Scheer, S. A., Crew Activity and Motion Effects on the Space Station, Report NAS 9-15800, Marshall Space Flight Center, Huntsville, Ala., 1986

[18] Amir, R. A. and Newman, D. J., “Research into the Effects of Astronaut Motion on the Spacecraft: A Review”, Acta Astronaut., 47:12 (2000), 859–869

[19] Prikl. Mat. Mekh., 76:4 (2012), 563–573 (Russian)

[20] Ahn, Y. T., Attitude Dynamics and Control of a Spacecraft Using Shifting Mass Distribution, Doctoral Dissertation, Pensylvania State University, University Park, Penn., 2012, 174 pp.

[21] Izv. Akad. Nauk. Mekh. Tverd. Tela, 2015, no. 6, 3–16 (Russian)

[22] Hwang, J., Attitude Stabilization of Spacecraft Using Moving Masses, Master Thesis, University of Texas at Arlington, Arlington, Tex., 2016, 65 pp.

[23] Virgili-Llop, J., Polat, H. C., and Romano, M., “Using Shifting Masses to Reject Aerodynamic Perturbations and to Maintain a Stable Attitude in Very Low Earth Orbit”, Spaceflight Mechanics 2016: Proc. of the 26th AAS/AIAA Space Flight Mechanics Meeting (Napa, Calif., Feb 2016), Adv. Astronaut. Sci. Ser., 158, eds. R. Zanetti, R. P. Russell, M. T. Ozimek, A. L. Bowes, Univelt, San Diego, Calif., 2016, 2129–2148

[24] Chesi, S., Gong, Q., and Romano, M., “Aerodynamic Three-Axis Attitude Stabilization of a Spacecraft by Center-of-Mass Shifting”, J. Guid. Control Dyn., 40:7 (2017), 1613–1626

[25] Virgili-Llop, J., Polat, H. C., and Romano, M., “Attitude Stabilization of Spacecraft in Very Low Earth Orbit by Center-of-Mass Shifting”, Front. Robot. AI, 6 (2019), 7

[26] Beletskii, V. V., Essays on the Motion of Celestial Bodies, Birkhäuser, Basel, 2001, 372 pp.

[27] Kholostova, O. V., “Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field”, Russian J. Nonlinear Dyn., 15:4 (2019), 505–512

[28] Zhong, X., Zhao, J., Yu, K., and Xu, M., Relative Equilibrium and Stability of a Three-Body Tethered Satellite in an Elliptical Orbit, Research Square, 2022, 16 pp.

[29] Duboshin, G. N., Celestial Mechanics: Analytical and Qualitative Methods, 2nd ed., rev. and enl., Nauka, Moscow, 1978, 456 pp. (Russian)

[30] Dokl. Akad. Nauk, 451:2 (2013), 164–167 (Russian)

[31] Beletsky, V. V., Reguläre und chaotische Bewegung starrer Körper, Vieweg + Teubner, Wiesbaden, 1995

[32] Uspekhi Mat. Nauk, 38:1 (229) (1983), 3–67 (Russian)

[33] Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1980, no. 6, 104–107, 120

[34] Burov, A. A. and Nikonov, V. I., “On the Nonlinear Meissner Equation”, Int. J. Non-Linear Mech., 110 (2019), 26–32