The swinging spring - Approximate analyses for low and very high energy. II

Details The swinging spring - Approximate analyses for low and very high energy. II The swinging spring - Approximate analyses for low and very high energy. II

Nov 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..359h&link_type=abstract

Celestial Mechanics, vol. 12, Nov. 1975, p. 359-382.

Computer Science

4

Energy Levels, Pendulums, Perturbation Theory, Springs (Elastic), Hamiltonian Functions, Libration, Numerical Integration, Oscillations, Periodic Variations

Scientific paper

The two families of periodic solutions emanating from the lower equilibrium of a planar spring-pendulum system are analyzed both at and near resonance. Hamiltonian perturbation theory is used to obtain approximate formulas for the characteristic and the period of the motion. As the energy is increased to very high levels, a circulatory and an almost rectilinear periodic motion persist. Expressions for the trace of a stability matrix are determined for both these solutions. Comparisons are made throughout with accurate results from numerical integration.

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