Hypothesis of the extremality of stable resonant motions

Details Hypothesis of the extremality of stable resonant motions Hypothesis of the extremality of stable resonant motions

Aug 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984primm..48..685k&link_type=abstract

Prikladnaia Matematika i Mekhanika (ISSN 0032-8235), vol. 48, July-Aug. 1984, p. 685-688. In Russian.

Physics

Celestial Mechanics, Classical Mechanics, Dynamic Stability, Resonant Vibration, Stable Oscillations, Trajectory Analysis, Approximation, Differential Equations, Extremum Values, Pendulums, Three Body Problem

Scientific paper

An approximate method is proposed for determining the mean values of the coordinate and time functions on trajectories of quasi-integrable dynamic systems. This method is used to average the force function and kinetic energy in the following problems: the motion of a material point near triangular libration points in the plane circular restricted three-body problem; and the motion of a physical pendulum with a rapidly oscillating suspension point near the lower and upper equilibrium positions. Considered to be applicable is the hypothesis of minimum averaged potential, kinetic, and total energies of the mechanical system in stable isolated synchronous motions. Particular reference is made to the motion of the Laplacean satellites of Jupiter and Uranus.

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