Third and fourth order resonances in Hamiltonian systems
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The stability of the origin of an autonomous Hamiltonian system is investigated when the system possesses a third or fourth-order resonance. H2, the quadratic part of H is H2=∑ni=1ωiJi and the resonance condition is ∑ni=1kiωi where the k ≥ 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 if ki≥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. © 1973 D. Reidel Publishing Company.
author list (cited authors)
Alfriend, K. T., & Richardson, D. L.