Diagrammatic theory of transition of pendulum like systems

Details Diagrammatic theory of transition of pendulum like systems Diagrammatic theory of transition of pendulum like systems

Jan 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19....3y&link_type=abstract

Celestial Mechanics, vol. 19, Jan. 1979, p. 3-29.

Mathematics

Probability

19

Gravitational Effects, Orbital Mechanics, Pendulums, Resonance, Spin-Orbit Interactions, Celestial Mechanics, Librational Motion, Mathematical Models

Scientific paper

Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

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