## Asymptotic Approaches in Nonlinear Dynamics: New Trends and ApplicationsThis book covers developments in the field of the theory of oscillations from the diverse viewpoints, reflecting the field's multidisciplinary nature. Addressing researchers in mechanics, physics, applied mathematics, and engineering, as well as students, the book gives an introduction to the state of the art in this area and to various applications. For the first time a treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with PadA(c) approximations is presented. Because of its wealth of interesting examples this book will prove useful as an introduction to the field for novices and a reference for specialists. |

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### Contents

Some General Principles of Asymptotology | 2 |

Discrete Systems | 13 |

Continuous Systems | 151 |

Copyright | |

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### Common terms and phrases

amplitude analysis analytical AP-portrait applied assume asymptotic analysis asymptotic approach asymptotic expansions asymptotic method averaging Awrejcewicz bifurcation boundary conditions boundary layer boundary value problem calculations characteristic equation coefficients components computation constant convergence coordinates corresponding cos2r curve damping defined deflection denotes depend described determined displacements eigenvalues elastic equation of system equations of motion exact solution example expression fc=i fc=o Fourier series frequency function governing equation homogeneous Hopf bifurcation initial conditions integral introduce isotropic Let us consider limiting system linear system masses modulation Nonlinear Dynamics nonlinear system normal vibrations numerical obtain the following ordinary differential equation Pade approximants periodic solution perturbation theory power series procedure resonance satisfied Sect separatrix shell small parameter soliton solved stability stationary points Substituting Taking into account Taylor series theory tion TPPA transform two-point Pade approximants variables vibro-impact zero