Theoretical analysis of selected trajectories inscribed by a ball freely rolling in a spherical cavity

Indirect monitoring of structures is significantly complicated when an artificial vibration absorber has to be taken into account. Knowledge of the absorber’s behaviour is necessary in order to correctly distinguish the response types obtained during an drive-by measurement. In this work, the mathematical model of the ball-type vibration absorber is used, which is based on the Lagrangian formalism. Three first integrals are identified when no external excitation nor damping is assumed. The paper illustrates the power of this approach, which enables a detailed analysis of free movement of the ball in the spherical cavity. Properties of several particular trajectories depending on initial conditions are presented