Orbital stability analysis using first integrals. (English. Russian original) Zbl 0734.70010
J. Appl. Math. Mech. 53, No. 6, 689-695 (1989); translation from Prikl. Mat. Mekh. 53, No. 6, 873-879 (1989).
Summary: A method is proposed for investigating the orbital stability of periodic solutions of normal systems of ordinary differential quations. The Lyapunov function is derived from the first integrals of the equations of the perturbed motion and the scalar product of the velocity of motion along the orbit and the perturbation vector. Lyapunov’s second method was first used in connection with orbital stability in order to study the phase trajectories of systems with two degrees of freedom.
MSC:
| 70G10 | Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics |
| 37C75 | Stability theory for smooth dynamical systems |
Keywords:
orbital stability; periodic solutions; systems of ordinary differential quations; Lyapunov function; first integrals; Lyapunov’s second method; phase trajectoriesReferences:
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