Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1753-1763 |
| Number of pages | 11 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 55 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1995 |
| Externally published | Yes |
ASJC Scopus subject areas
- Applied Mathematics