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IMA Journal of Applied Mathematics 1978 22(4):383-399; doi:10.1093/imamat/22.4.383
© 1978 by Institute of Mathematics and its Applications
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A General Theory of Resonance Between Weakly Coupled Oscillatory Systems

W. CHESTER

Department of Mathematics, University of Bristol, University Walk Bristol BS8 1TW

Resonant oscillations are investigated between several fully non-linear oscillatory systems which are subject to a weak coupling. The equations of motion are obtained from a Hamiltonian which is first expressed in terms of angle action variables, and then averaged. It is shown that this results in a reduced set of equations, the reduction depending on the number of resonances between the various systems. For example a resonance in a system with two degrees of freedom results in equations which are mathematically equivalent to those for one degree of freedom. The theory is illustrated by application to the forced oscillations of a simple pendulum and to the resonant interaction between the two modes of oscillation of a double pendulum.


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