3: Nonlinear Systems
- Page ID
- 105975
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- 3.10: Appendix - Period of the Nonlinear Pendulum
- Previously, we saw that the solution of the nonlinear pendulum problem can be found up to quadrature. In fact, the integral solutions can be transformed into what is know as an elliptic integral of the first kind. We will rewrite our result and then use it to obtain an approximation to the period of oscillation of our nonlinear pendulum, leading to corrections to the linear result found earlier.
Thumbnail: A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. (Public Domain; Catslash).