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Note to the asymptotic behaviour of solutions of damped pendulum equations under forcing. (English) Zbl 0763.34038

The author examines the pendulum equation \(\ddot x+a\dot x+b\sin x=p(t)\) with \(a\) and \(b\) constant and \(p(t)\) a continuous function. Several theorems concerning stability and boundedness of solutions are presented. Conjectures about extensions of these theorems are also given. — The paper is by its nature theoretical. It could be of interest and use to those working in the foundation of nonlinear oscillations and in stability theory.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K20 Stability for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
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