Determination of coupled sway, roll, and yaw motions of a floating body in regular waves.
On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations. Furthermore,...