Spring Pendulum

The Spring Pendulum is a three-dimensional dynamical system. This means that it has three degrees of freedom. Again, you can move the pendulum around by clicking and dragging on it.

Sometimes, this Spring Pendulum spins out of control, due to an amplification of numerical errors. This happens for example when you make one of the masses equal to zero. If the system becomes unstable or crashes, you can restart the simulation by clicking the "Restart" button.

A new feature of the applet, which is demonstrated here, is the ability to switch forced preservation of energy on and off. Normally, we force the total energy of the system to remain constant. Click on the "Constrain Energy" button to switch off energy preservation. The total energy of the system will now fluctuate slowly, due to the numerical errors that arise in the solution of the differential equations. The method used for solving the differential equation is a fourth-order Runge-Kutta method, which gives relatively good, though not perfect, results.

Your browser does not run this applet, for some reason.
Here is what it would look like:

  1. Double Pendulum,
  2. Double Spring,
  3. Spring Pendulum.

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Peter Selinger / Department of Mathematics and Statistics / Dalhousie University
selinger@mathstat.dal.ca / PGP key
Updated June 13, 1999