Mathematics
Scientific paper
Mar 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978zamm...58..121m&link_type=abstract
Zeitschrift für angewandte Mathematik und Mekhanik, vol. 58, Mar. 1978, p. 121-132. In German.
Mathematics
Asteroids, Celestial Mechanics, Orbit Perturbation, Three Body Problem, Transient Oscillations, Forced Vibration, Hamiltonian Functions, Harmonic Excitation, Jupiter (Planet), Libration, Nonlinearity, Nonstabilized Oscillation, Secular Variations, Stable Oscillations
Scientific paper
Using the method of secular perturbations within the restricted problem of three bodies the paper presents the motions of an asteroid revolving with nearly half the period of Jupiter as small oscillations about a steady circular motion. It is shown that the motions have the characteristic features of both forced and parametrically excited nonlinear vibrations with softening restoring force. In particular there are stable and unstable stationary vibrations corresponding with the periodic solutions and transient vibrations corresponding to the librational solutions of the restricted problem of three bodies.
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