A system of two coupled pendula is an example of a Hamiltonian system with two degrees of freedom. Rott considered such a system in the presence of 1:2 resonance and observed a phase-locking phenomenon. In this paper this phenomenon is explained by means of Duistermaat's method of bringing a Hamiltonian system with two degrees of freedom into standard form. His theory is based on Mather's theory of stability of differentiable mappings. A transparent geometrical picture is obtained in the phase space. In particular, a criterion of the phase-locking phenomenon is provided based on this picture.
ASJC Scopus subject areas
- Applied Mathematics