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A generalized scheme for constructing Lyapunov functions from first integrals. (English. Russian original) Zbl 1025.34047
J. Appl. Math. Mech. 65, No. 2, 195-204 (2001); translation from Prikl. Mat. Mekh. 65, No. 2, 199-210 (2001).
The author proposes some heuristic scheme of construction of Lyapunov $$v$$-functions in terms of the first integrals of the equations of motion under consideration. General results are applied to the investigation of asymptotic stability of the zero solution to a system with two degrees of freedom at resonance 1:1.

MSC:
 34D20 Stability of solutions to ordinary differential equations 70K28 Parametric resonances for nonlinear problems in mechanics 70K20 Stability for nonlinear problems in mechanics