Third and fourth order resonances in Hamiltonian systems |
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| Authors: | Kyle T Alfriend David L Richardson |
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| Institution: | (1) Dept. of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y., U.S.A. |
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| Abstract: | 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
i
J
i
and the resonance condition is n
i=1
k
i
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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| Keywords: | |
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