On the motion of the pendulum on an ellipse

In the present study, the motion of a pendulum on an ellipse is considered. The supported point of this pendulum moves on an elliptic path while the end point moves with arbitrary angular displacements. Applying Lagrange's equation, the equation, of motion, is obtained in terms of a small parameter epsilon. This equation represents a quasilinear system of second order which can be solved in terms of a generalized coordinate phi.