Orbits on a Concave Frictionless Surface
NAVAL ACADEMY ANNAPOLIS MD DEPT OF PHYSICS
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The equations of motion of a puck sliding frictionlessly inside a parabolic bowl can be straightforwardly deduced using the conservation laws of mechanical energy and angular momentum. But the solution of these equations requires that they be recast into the form of Newtons second law. The simple example of a ball in vertical freefall illustrates why this is necessary and how to perform the conversion. The method is then applied to the richer problem of a puck gliding on a paraboloidal surface for which the nonlinear equations require numerical solution. A rich variety of orbital patterns of the puck is found.
- Operations Research