Lyapunov's methods, the two main methods of studying the stability of motion, proposed by A. M. Lyapunov (1892). In essence each of Lyapunov's methods covers a set of approaches united by a common idea. The first of Lyapunov's methods rests on finding and studying the solutions of the equations of the so-called perturbed motion, that is, of motion that for some reason (for example, after a chance jolt) differs from the unperturbed motion under consideration. The second (or direct) of Lyapunov's methods is the more widely used and consists in studying the stability of motion with the help of certain specially introduced functions, called Lyapunov functions.