Third and Fourth Order Resonances in Hamiltonian Systems

Details Third and Fourth Order Resonances in Hamiltonian Systems Third and Fourth Order Resonances in Hamiltonian Systems

Jun 1973

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973cemec...7..408a&link_type=abstract

Celestial Mechanics, Volume 7, Issue 4, pp.408-420

Physics

4

Scientific paper

The stability of the origin of an autonomous Hamiltonian system is investigated when the system possesses a third or fourth-order resonance.H 2, the quadratic part ofH isH 2=∑n i=1 ω i J i and the resonance condition is ∑n i=1 k i ω i where thek ⩾ 0,i = 1, 2, ...,n are the natural or fundamental frequencies. It is shown that the only case in which the origin can be unstable is ifk i≥0,i=1,2,...,n. The condition for instability is then given in terms of the coefficients of the higher order terms in the Hamiltonian. The transfer of energy between modes is also investigated when a near-resonant condition exists.

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