The elastic vibrations of the cable system

The motion of elastic cable system around the center of mass is considered. Cable system consists of two end objects and an imponderable elastic cable which is in an unrolled position. The center of mass of a system moves on an elliptical trajectory. By means of Lagrange's equations of the second kind, the equations of motion of the elastic cable system are constructed, as an independent variable the angle of true anomaly is chosen. The analytical solution describing elastic vibrations of the stretched cable is found.