Chaotic motions in the dynamics of space tethered systems. 3. Influence of energy dissipation

1Pirozhenko, AV
1Institute of Technical Mechanics of the NAS of Ukraine and SSA of Ukraine, Dnipro, Ukraine
Kosm. nauka tehnol. 2001, 7 ;(5-6):013-020
Section: Spacecraft Dynamics and Control
Publication Language: Russian
Abstract: 
The determined-chaos phenomenon in the dynamics of space tethered systems under the action of exterior dissipative forces is examined with the help of the numerical integration of the model problem equations of motion of an orbital pendulum with a periodically varying boom length. The dissipative forces are simulated as forces of viscous friction with the exterior medium. We show that the random synchronization of motions strange attractors may exist. Mechanical images of stochastic motions under the action of dissipative forces are constructed. The determined-chaos phenomenon is analyzed from the point of view of the history and problems of the classical mechanics.
Keywords: determined chaos, dissipative forces, tethered systems
References: 
1. Arnold V. I. Mathematical Methods of Classical Mechanics, 3rd ed., 472 p. (Nauka, Moscow, 1983) [in Russian].
2.  Beletskii V. V. Essays on the motion of bodies in space, 2nd rev. and enlarg. ed., 430 p. (Nauka, Moscow, 1977) [in Russian].
3. Bergé P., Pomeau Y., Vidal Ch. Order within Chaos. Towards a Deterministic Approach to  Turbulence, 386 p. (Mir, Moscow, 1991) [in Russian].
4.  Pirozhenko A.V. Chaotic motions in the dynamics of space tethered systems. 1. Analysis of the problem. Kosm. nauka tehnol., 7 (2-3), 83— 89 (2001) [in Russian].
5.  Pirozhenko A.V. Chaotic motions in the dynamics of space tethered systems. 2. Mechanical image of the phenomenon. Kosm. nauka tehnol., 7 (2-3), 90—99 (2001) [in Russian].
6.  Subbotin M. F. Introduction to Theoretical Astronomy, 800 p. (Nauka, Moscow, 1968) [in Russian].
7.  Shuster G. Deterministic Chaos: An Introduction, 240 p. (Mir, Moscow, 1988) [in Russian].
8.  Lorenz E. N. Deterministic nonperiodic flow. J. Atmos. Sci., 20, P. 130 (1963).

9.  Molchanov A. M. The resonant structure of the solar system. The law of planetary distances. Icarus, 8 (2), 203—215 (1968).