Titlebook: Nonlinear Oscillations and Waves in Dynamical Systems; P. S. Landa Book 1996 Springer Science+Business Media Dordrecht 1996 Degrees of fre

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Non-conservative Hamiltonian systems and dissipative systemsThe simplest mathematical models of a non-linear oscillator with a force of friction and an external action are: ., ..

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Natural oscillations of non-linear oscillatorsAssuming that the pendulum shown in Fig 5.1. oscillates in a single plane and ignoring friction forces, we obtain the following equation for the angle of rotation .: . where . is the mass of the ball, and . is the length of the thread.

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Natural oscillations in systems of coupled oscillatorsThe general theory of normal oscillations in linear systems with constant parameters is adequately covered in many books (for example, see [Bulgakov, 1954; Strelkov, 1964]). So here we call attention only to the fundamental tenets of this theory and to some concrete results.

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Oscillations of a non-linear oscillator excited by an external forceLet us consider a non-linear oscillator driven by a periodic external force with period .. Let the equation of this oscillator be . where . is a periodic function that can be represented in the form of a Fourier series:

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