The Analysis of Rotated Vector Field for the Pendulum

Abstract

The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$ and the periodic solution, and a conclusion that the critical value of $\beta$ is a fixed one in the over damping situation. These results are of practical significance in the study of charge-density waves in physics.

arXiv comment11 pages With 8 figures. A mathematical focus version separated from cond-mat/0702061. cond-mat/0702061 is replaced with a physics focus version. In Ver.2, some sentences are revised on rhetoric, and the bibliography is renewed

References in corpus (1)

• The analysis on the single particle model of CDW

Cited by in corpus (1)

• The analysis on the single particle model of CDW