Titlebook: Oscillators and Oscillatory Signals from Smooth to Discontinuous; Geometrical, Algebra Valery N. Pilipchuk Book 2023Latest edition Springer

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Introduction,ther intuitive, they nevertheless provide hints on selecting complementary generating models and the corresponding analytical tools. The core concept is in the assumption that a technical simplicity of mathematical formalisms is due to their hidden links with subgroups of rigid-body motions represen

BANAL

Smooth Oscillating Processes,orresponding technical implementations usually employ the harmonic oscillator as a generating model. The description focuses on such ideas and technical details that are further combined with nonsmooth methods. The related procedures of the asymptotic integration usually include the stage of a preli

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NSTT for Linear and Piecewise-Linear Systems,lly close to nonsmooth ones. Such cases are known to be most difficult for analyses because different quasi-harmonic methods are already ineffective, whereas the nonsmooth mapping is still inapplicable. It is quite clear however that the nonsmooth arguments can be introduced regardless of the streng

Charlatan

Periodic and Transient Nonlinear Dynamics Under Discontinuous Loading,own two-variable procedure, the differential equations for the slow dynamics emerge from the boundary conditions eliminating discontinuities instead of resonance terms. For illustrating purposes, an impulsively loaded one degree-of-freedom model with cubic damping and no elastic force is considered.

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Strongly Nonlinear Vibrations,rms, such algorithms approximate temporal mode shapes of vibrations by polynomials and other simple functions of the triangle wave. In order to develop the algorithms, the triangle wave is introduced into dynamical systems as a new temporal argument. The corresponding manipulations with dynamical sy

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Strongly Nonlinear Waves,resented by the infinite linear string on elastic foundation. In this case, the carrying wave can be approximated by polynomials or other elementary functions of the triangle wave based on the algorithms of the previous chapter. Then the differential equations for slow varying modulations are derive

Institution

Impact Modes and Parameter Variations,ct modes gives another impact mode. The number of impact modes depends on the number of constraints and therefore can significantly exceed the number of degrees of freedom. The corresponding manipulations with impact modes become possible due to the availability of closed-form exact solutions obtain