INVESTIGATION OF NONLINEAR OSCILLATIONS WITH THE AID OF lyapunov functions,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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In Ch. 1, Autonomous Systems, the author considers the system of two equations. The conditions for the existence and stability of a periodic solution are established. The following method is used we convert to polar coordinates and seek the Lyanunov function V in implicit form. Criteria for the stability or instability of the sought cycle are also established in the form of the function Lsubscript 1 V, and a method for finding an approximate equation of limit cycles is indicated estmates of the value of the small parameter Mu, for which the theory being developed can be used, are given. The author then considers cases in which studies of more general systems of two equations can be reduced to the study of previously analyzed particular cases. At the end of the chapter the author discusses the feasibility of using Lyapunov functions to find stationary generally speaking, nonperiodic oscillations for multidimensional systems as well, but gives no computations. Ch. 2, Nonautonomous Systems, briefly reviews the theory of obtaining stationary oscillations.
- Numerical Mathematics