Lyapunov Stability Of Tethered Dumbbell Satellites In Elliptical Orbit

Authors

  • Joydip Ghosh RDS COLLEGE, MUZAFFARPUR
  • Sangam Kumar

DOI:

https://doi.org/10.12723/mjs.69.2

Keywords:

Tether, Solar light pressure, Satellites, Shadow, Oblateness, Geomagnetic field

Abstract

This paper represents the equilibrium positions and stability of two artificial satellites connected by light, flexible, and elastic long tethers under the combined effect of several classical perturbative forces in an elliptical orbit. The tether may be conducting or non-conducting. In our problem, it is taken as non-conducting in nature. We have treated the problem by taking five perturbative forces on the system simultaneously. Three perturbations exist due to the influences of the earth, namely geomagnetic fields, shadows, and oblateness. The other perturbations are due to the elasticity of the cable and solar light pressure. The effect of air resistance is neglected, considering the satellites as high-altitude satellites. To determine the stability of the satellites, we have used the Lyapunov method. The dynamical behaviors of the satellites are represented by differential equations. Based on analytical analysis of the differential equations of motion, we get the equilibrium positions of the system concerned in elliptical orbit. Lyapunov method gives the equilibrium position as unstable as expected.

References

P. Williams, Deployment/retrieval optimization for flexible tether satellite system, Nonlinear Dyn, 52(1-2), 159-179, (2008)

A. Steindl, Optimal deployment of a tethered satellite using tension control, Int. Fed. Autom. Control Papers online, 48 (1), 53-54 (2015)

K.D. Kumar, Review of dynamics and control of non-electrodynamic tethered satellite systems, J. Spacecr. Rockets 43(4), 705-720 (2006)

A.K. Mishra, M.S. Nixon, V.J. Modi, Nonlinear dynamics of two-body tethered satellite systems: constant length case. J. Astronaut. Sci. 49(2), 219-236 (2001)

M.L. Cosmo, E.C. Lorenzini, Tethers in space handbook, 3rd edn. NASA Marshal Space Flight Center, Washington (1997)

V.V. Beletsky, E.M. Levin, Dynamics of space tether systems, Advances in the Astronautical sciences, Vol. 83 (1993)

A.A. Burov, H. Troger, The Relative equilibria of an orbital pendulum suspended on a tether, Journal of Applied Mathematics and Mechanics, 64 (5) 723-728 (2000)

M.R. Liberzon, Essay on the Absolute stability Theory, Automation and Remote Control, 67, 10, 1610-1644 (2006)

B.S. Yu, H. Wen, D.P. Jin, Review of deployment technology for tethered satellite systems, Acta Mechanica Sinica, (2017) https://doi.org/10.1007/s10409-018-0752-5

S. Kumar, S. Kumar, Equilibrium positions of a cable- connected satellites system under several influences, International Journal of Astronomy and Astrophysics, China, 06, 288-292 (2016)

B.S. Yu, S.D. Xu, D.P. Jin, Chaos in a tethered satellites system induced by atmospheric drag and earth’s oblateness, Nonlinear Dyn, (2020) https://doi.org/10.1007/s11071-020-05844-8

S. Kumar S and J. Ghosh, Elastic cable-connected satellites system under several influences of general nature: equations of motion in elliptical orbit, Sci. and Tech. Journal 9(1) 14-20 (2021) https://doi.org/10.22232/stj.2021.09.01.03

J. Ghosh and S. Kumar, Jacobean integral of planar tethered dumbbell satellites in elliptical orbit, IJPAS, Vol 09 (11) (2022)

Additional Files

Published

2024-07-15