Stability in the double resonance problem

Details Stability in the double resonance problem Stability in the double resonance problem

Jan 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35....9l&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 35, Jan. 1985, p. 9-17.

Physics

3

Celestial Mechanics, Motion Stability, Orbit Perturbation, Pendulums, Resonance, Artificial Satellites, Differential Equations, Equilibrium Equations, Hamiltonian Functions, Roots Of Equations, Satellite Orbits

Scientific paper

The 2-pendulum analogy of Ferraz-Mello (1979) to the ideal double-resonance problem of celestial mechanics is investigated analytically, with a focus on the infinitesimal stability of the equilibrium solutions (in a Liapunov sense) up to fourth order. The theorems of Arnold and of Khazin (1969) are applied to the nonlinear terms for cases with purely imaginary characteristic roots, and sample results are presented graphically. The implications of the double-resonance problem for the motion of sun-synchronous satellites at near-critical inclination are indicated.

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