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Nonlinear oscillations of the vertical plane swinging spring pendulum in the resonance case are studied (frequencies ratio regarding horizontal and vertical directions is equal to 1:2). Square and cubic terms of the Hamiltonian are taken into account. Novel normal form method, i.e., the so called invariant normalization is applied to solve the stated problem. Full system of integrals exhibits equations...
We propose a novel method to analyze the dynamics of Hamiltonian systems with a periodically modulated Hamiltonian. The method is based on a special parametric form of the canonical transformation $${\bf q},{\bf p}\to {\bf Q},{\bf P}$$ , $$H(t,{\bf q},{\bf p})\to \bar H(t,{\bf Q},{\bf P})$$ $$\displaylines{ \begin{array}{c} \left\{ \begin{array}{c} {\bf q}={\bf x}-\displaystyle\frac12\Psi_{\bf...
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