Uniform rotations of a variable-length pendulum

Abstract

Let a pendulum represent the material point P of a weight mg attached to the end of a weightless inex tensible string. The motion occurs in a uniform gravity field in the fixed vertical plane Oxy passing through a motionless point O (Fig. 1). The string length OP is the set function of time t: = . It is assumed that the string remains stretched during the pendulum motion; i.e., the coordinates x and y of the point P satisfy the equation of the supporting geometrical constraint