• define the EOM for the mathematical pendulum
• plot the direction field of the EOM
• determine the solutions for given initial conditions
• plot the solutions in phase space
• add the heteroclinic solutons
• merge different plots and save them
• determine the time evolution for the heteroclinic solution

For more information you can take a look at a screenshot of the notebook — or you give it a try and

I am always very grateful for suggestions:

• need for additional comments and explanation
• possibilities for alternative, potentially more elegant solutions
• requests for other worksheets that introduce and explain further features of Sage or explore topics relevant for our course

Please send your notebooks by email to me, or post a comment in this discussion forum: