Resonance capture in certain nearly Hamiltonian systems

Details Resonance capture in certain nearly Hamiltonian systems Resonance capture in certain nearly Hamiltonian systems

Mar 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975jde....17..361m&link_type=abstract

Journal of Differential Equations, vol. 17, Mar. 1975, p. 361-374.

Mathematics

2

Celestial Mechanics, Differential Equations, Hamiltonian Functions, Orbit Calculation, Spin Resonance, Angular Velocity, Coordinate Transformations, Elliptical Orbits, Existence Theorems, Fourier Series, Planetary Rotation

Scientific paper

The mathematical cases studied in the current work lie between two extremes: when the equation theta-double dot = 0 is perturbed to a nonintegrable Hamiltonian system, and when the perturbation contains substantial friction. The problem is to determine the possible 'final values' of the angular velocity omega and to show how their number increases as the friction goes to zero. The application motivating the undertaking is to planetary spin resonance, in which the periodic orbit of a planet or satellite about its primary is given and the spin of the planet on its axis, assumed normal to the plane of the orbit, is studied.

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