A comparison of three methods of constructing Lyapunov functions

Chetayev's effective method 1] for constructing Lyapunov functions in the form of a set of first integrals of the equations of perturbed motion has been widely used since the 1950s in Russia. In the 1980s the energy-Casimir method 2] was developed in the U.S.A. as well as the energy-momentum method 3], employed for Hamiltonian systems. A comparison of these methods for systems with a finite number of degrees of freedom has shown that the energy-Casimir method is a more complicated version of Chetayev's method, while the energy-momentum method is essentially the Routh-Lyapunov method 4,5], stated in modern geometrical language. Some examples are considered.