Reguläre und chaotische Bewegung starrer Körper

Abstract

Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlages unzulässig und strafbar. Das gilt besonders fürVervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen.

The necessary conditions for the stability of steady motions of systems with constraints produced by large potential forces

“…Then, by virtue of expressions (5.4) and (5.5) in the class of triangular motions the tether stretches, and the results related to the existence and stability of steady motions, obtained previously in [15,16] for a constraint realized using a rod, remain true for a constraint realized using a tether.…”

“…This problem was considered in [15] (see also [16]) on the assumption that the points are connected by inextensible weightless rods and form a dumbell; it was shown, in particular, that there are regions in parameter space such that, for appropriate values of these parameters, gyroscopic stabilization of "triangular" steady motions is possible.…”

Chaotic attitude motion and its control of spacecraft in elliptic orbit and geomagnetic field

“…The chaotic attitude motion exists in di erent kinds of spacecraft [1][2][3][4][5][6][7][8]. Beletsky et al [9,10] discussed the chaotic motion of a magnetic spacecraft in circular polar orbit without damping and gravitational torque numerically. Cheng, Chen and Liu [11][12][13] studied the chaotic motion of a magnetic spacecraft in a circular orbit by using the Melnikov method and found that the onset of chaos is characterized by the intermittence as the increase of the magnetic torque.…”

Chaotic motion of an asymmetric gyrostat in the magnetic field of the earth

“…Both numerical and analytical methods have been employed. Beletsky [1] discussed the chaotic phenomena in the libration of rigid satellites under various actions such as gravitational force, magnetic force and sunlight pressure by using the numerical method. As for analytical aspect, an effective technique is Melnikov's method [2], which provides a criterion for existence of chaotic motion in the sense of Smale's horseshoe for a one-degree of freedom system.…”