Analytic continuation of quasi-periodic orbits from non-linear periodic modes

Details Analytic continuation of quasi-periodic orbits from non-linear periodic modes Analytic continuation of quasi-periodic orbits from non-linear periodic modes

Dec 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..587h&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 4, p. 587-617

Astronomy and Astrophysics

Astronomy

1

Orbit Calculation, Orbit Perturbation, Orbital Mechanics, Periodic Variations, Perturbation Theory, Propagation Modes, Rotation, Differential Equations, Equations Of Motion, Jacobi Integral, Nonlinear Systems, Series Expansion

Scientific paper

A new theory is formulated for the analytic continuation of quasi-periodic orbits from non-linear, periodic modes of a two degree-of-freedom system in rotating coordinates. Formal solutions of the equations of motion are developed in series expansions, with the non-linear modes as reference solutions. Conditions are determined on the existence and boundedness of the time-dependent coefficients of the velocity field. Boundedness properties of the orbits are specified by an orbit function derived from the Jacobi integral.

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