The energetic/variational interpretation of Poincaré's criterion for the orbital stability of limit cycles of autonomous systems
A proof of the Poincaré criterion for orbital stability of limit cycles of autonomous systems is given by \textit{J. J. Stoker} [Nonlinear vibrations in mechanical and electrical systems (1950; Zbl 0035.396)] based on phase-space methods. A version of the proof has also been presented by \textit{S. W. McCuskey} [An introduction to advanced dynamics (1959; Zbl 0082.171)]. According to the author the only other existing proof is based on the theory of characteristic exponents [see \textit{R. E. Mickens}, An introduction to nonlinear oscillations (1981; Zbl 0459.34002)]. The author summarizes the Stoker/McCuskey proof, and then developes a new proof based on Lagrangian/Hamiltonian variational principles.
scientific article; zbMATH DE number 4003576