Ideal Resonance Problem: the Post-Post-Pendulum Approximation

Details Ideal Resonance Problem: the Post-Post-Pendulum Approximation Ideal Resonance Problem: the Post-Post-Pendulum Approximation

May 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..83..275f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 83, Issue 1, p. 275-289 (2002).

Astronomy and Astrophysics

Astronomy

Ideal Resonance Problem, Small-Amplitude Libration

Scientific paper

Explicit construction of the solutions of the Hamiltonian system given by H = H0(J) - ɛ A(J) cos θ (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order $O(\root{4}\of{\varepsilon})$. The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed.

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