Computational Methods in Physics ASU Physics PHY 494

12 ODEs: Applications

14 Mar 2019

After implementing a number of integrators for ODEs we are now in the position to solve some practical problems:

  • projectile movement with air resistance
  • realistic movement of a spinning baseball

For the problem that you should solve during the class, get the notebook1 12-ODE-applications-students.ipynb and see notebook 12-ODE-applications.ipynb for the full solution.2

The baseball problem was live-coded from scratch during class and the notebook baseball_solution.ipynb2 is a cleaned-up and commented solution. The lesson showed how

  1. to define the physical problem (obtain trajectory of a baseball with spin and air resistance)
  2. to derive the underlying equations (Newton's equations of motions and the forces acting on the ball)
  3. to adapt an algorithm to solve the equations (use RK4 for integrating the ODEs and express the problem in ODE standard form so that one can use ode.rk4())

  4. to visualize and discuss the results (plot trajectories and assess the influence of spin)

    Trajectories of a baseball

Resources

  • Computational Modelling: Chapter 3

Footnotes

  1. As usual, git pull the resources repository PHY494-resources to get a local copy of the notebook. Then copy the notebook and all other code into your work directory in order to complete the exercises. ↩

  2. Notebook will be posted after class; in the mean time look at the student notebook. ↩ ↩2

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