## Order and Chaos: Understanding the double pendulum |

**Krishnan Shanmuganandham**

Union College

April 15, 2005

4:30 pm

Golub 105

Pizza and drinks will be served

The double pendulum is a relatively simple classical system that has intrigued physicists and mathematicians for centuries.It arises in the world of sports every time a golfer swings a club or a baseball player hits a ball. Due to its interesting behavior of exhibiting both chaotic and periodic motion it has come under a lot of study. The type of motion depends on the parameters of the system such as the masses of the bobs, the lengths, and the initial angles and velocities of the pendulums. The goal is to characterize the type of motion as a function of the starting configuration. To simplify this multi-variable system we look at different starting angles of the system for a given double pendulum at rest. `We obtain a numerical solution to the system by two methods: the Euler-Lagrange differential equation and the Runge-Kutta method of the fourth order. The plots of the angles of each pendulum for different starting positions gives us interesting insights into the type of motion.

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