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Plane Rigid Pendulum

Developed by K. Roos - Published July 31, 2016

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, MATLAB, Python, Spreadsheet, and Easy Java Simulations
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**);

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Credits and Licensing

K. Roos, "Plane Rigid Pendulum," Published in the PICUP Collection, July 2016.

The instructor materials are ©2016 K. Roos.

The exercises are released under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license