Plane Rigid Pendulum

Developed by K. Roos

Easy JavaScript Simulation by Fremont Teng and Loo Kang Wee

In this set of exercises the student builds a computational model of a simple plane rigid pendulum using the Euler-Cromer numerical scheme. The student is guided to explore the accuracy of the computational model, and to compare the computational results with the popular analytical solution for the pendulum via the small angle approximation. Damping and driving terms are added to the computational model, and the student is lead to discover chaotic trajectories in phase space.

Subject Area | Mechanics
Levels | First Year and Beyond the First Year
Available Implementations | C/C++, Fortran, IPython/Jupyter Notebook, Mathematica, Octave*/MATLAB, Python, Spreadsheet and Easy JavaScript Simulation
Learning Objectives | Students who complete this set of exercises will be able to build a computational model of a simple rigid pendulum using the Euler-Cromer algorithm (Exercise 1); to produce graphs of the angular displacement and angular velocity of the pendulum as a function of time from the results of their computational model (Exercises 1-5); to assess the accuracy of the computational results of their model (Exercises 1); to identify the limitations of the small angle approximation for the plane pendulum (Exercises 2) to produce phase space plots for various system parameters (Exercises 3); and to produce chaotic phase space trajectories by varying model parameters (Exercise 4 and 5);