Capture into resonance - an extension of the use of adiabatic invariants

Details Capture into resonance - an extension of the use of adiabatic invariants Capture into resonance - an extension of the use of adiabatic invariants

May 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27....3h&link_type=abstract

Celestial Mechanics, vol. 27, May 1982, p. 3-22.

Mathematics

Probability

89

Capture Effect, Celestial Mechanics, Invariance, Mechanical Devices, Orbital Mechanics, Resonance, Trajectory Analysis, Adiabatic Conditions, Equations Of Motion, Long Term Effects, Probability Theory, Solar System

Scientific paper

It is noted that the theory of the adiabatic invariant predicts the long-term evolution of mechanical systems with slowly varying parameters. The theory, however, is not valid when the system goes across a critical trajectory. The importance of this case derives from the fact that it can lead to capture into resonance. Analyzing the motion in the vicinity of the critical trajectory, general formulas are given for the probability of capture and it is shown that, in general, the adiabatic invariant is conserved. Allowance is made here for the geometrical discontinuity in its definition at the critical orbit.

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