Compass Needle in Uniform and Rotating Magnetic Fields
A compass needle undergoes forced oscillations under the influence of a uniform magnetic field and a rotating magnetic field with angular velocity (black arrow). The compass needle has a moment of inertia , a friction constant , and a magnetic moment ℳ. This is a simple example of a system that shows chaotic motion. In a real experiment it is impossible to repeat a particular motion from initial conditions and because the system is chaotic.
The differential equation to solve is .