Numerical study of periodic orbit properties in a dynamical system with three degrees of freedom

Details Numerical study of periodic orbit properties in a dynamical system with three degrees of freedom Numerical study of periodic orbit properties in a dynamical system with three degrees of freedom

Nov 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..319m&link_type=abstract

Celestial Mechanics, vol. 28, Nov. 1982, p. 319-343. Research supported by the Swiss National Science Foundation.

Statistics

Computation

39

Degrees Of Freedom, Motion Stability, Orbital Mechanics, Orbital Position Estimation, Periodic Variations, Asymptotic Methods, Celestial Mechanics, Position Errors, Stochastic Processes

Scientific paper

The study outlined here has three purposes. The first is to make use of the knowledge gained of periodic orbits in bidimensional systems in order to investigate the prolongation of such orbits in systems with three degrees of freedom. The second is to investigate the influence exerted on the position and stability of p.o. by the variation of the higher-order terms in the potential. The third purpose is to examine the vicinity of unstable p.o. in the four-dimensional space of section in order to observe the effect of instability upon the degree of stochasticity in tridimensional systems. After presenting the potential used and the methods of numerical computations, the main results, together with some illustrative stereoscopic pictures of periodic orbits, are described. Some representations, in the four-dimensional space of section, of invariant surfaces located near periodic orbits and of asymptotic curves emanating from the main unstable p.o. are then shown.

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