The elliptic-parabolic motion of an elastic pendulum is the subject of current study. The elasticity is either provided by a single spring or an elastic cable. The motion is called elliptic-parabolic since the point mass takes the elliptical path when viewed from the top and the parabolic path when viewed from the side. Such motion can be initiated when an initial displacement and and an initial velocity are given in the perpendicular directions. The fully nonlinear analysis shows that the elliptical path precesses. In this paper, perturbation analysis is used to obtained the precession rate for the discrete and continuous pendulum.

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