The Analysis of Rotated Vector Field for the Pendulum
Dynamical Systems
2012-05-15 v2 Classical Analysis and ODEs
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 and the periodic solution, and a conclusion that the critical value of is a fixed one in the over damping situation. These results are of practical significance in the study of charge-density waves in physics.
Cite
@article{arxiv.0807.3288,
title = {The Analysis of Rotated Vector Field for the Pendulum},
author = {Lian-Gang Li},
journal= {arXiv preprint arXiv:0807.3288},
year = {2012}
}
Comments
11 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