The analysis of rotated vector field on the pendulum equation

Details The analysis of rotated vector field on the pendulum equation The analysis of rotated vector field on the pendulum equation

2008-07-21

arxiv.org/abs/0807.3288v1

Mathematics

Dynamical Systems

11 pages With 8 figures. A mathematical focus version separated from cond-mat/0702061. Cond-mat/0702061 is replaced with a phy

Scientific paper

The driven, damped pendulum equation is a mathematical model of pendulum. It is a nonlinear differential equation which is non-integrable. By the method of rotated vector field, this paper obtains the relation between the external drive $\beta$ and the periodic solution. An other conclusion is that the critical value of $\beta$ remains fixed in the over damping situation. These results is very useful in the study of charge-density wave in physics

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