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Plane Rigid Pendulum
Developed by Kelly Roos  Published July 31, 2016
DOI: 10.1119/PICUP.Exercise.RigPend
In this set of exercises the student builds a computational model of a simple plane rigid pendulum using the EulerCromer 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 EulerCromer 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 15**);
 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
Kelly Roos, "Plane Rigid Pendulum," Published in the PICUP Collection, July 2016, https://doi.org/10.1119/PICUP.Exercise.RigPend.
DOI: 10.1119/PICUP.Exercise.RigPend
The instructor materials are ©2016 Kelly Roos.
The exercises are released under a Creative Commons AttributionNonCommercialShareAlike 4.0 license