  In this paper, the underlying energy flow in rocking dynamics of rigid blocks
is utilized to elucidate their response details and overturning conditions.
Based merely on the law of the conservation of energy, the exact criteria for a
rigid block to overturn in the free vibration regime are established for the
first time in the context of both nonlinear and linear theory. That is, if the
initial conditions of the free oscillation regime fall within the prescribed
stable libration region, then it is a priori determined that the block will not
overturn and vice versa. The analytical solution to the nonlinear free rocking
problem is also derived, utilizing integration techniques originating from the
solution of the nonlinear pendulum. Additionally, pulse-type overturning
spectra are constructed easily by numerical integration of the equation of
motion only during the pulse duration. If the block does not topple during the
forced regime, the angle and angular velocity at the end of the excitations are
employed to assess immediately the safety or unsafety of the block using the
exact overturning nonlinear criterion. Finally, new insights into the stability
regions of the overturning spectra are illuminated and explained in detail
using a color mapping.
