Valtancoli in his paper entitled (P. Valtancoli, Canonical transformations and minimal length, J. Math. Phys. 56, 122107 2015) has shown how the deformation of canonical can be made compatible with deformed Poisson brackets. Based on this work through an appropriate transformation, we solve problem one dimensional (1D) damped harmonic oscillator at classical limit Snyder-de Sitter (SdS) space. ...

We study the large-time behaviour of the nonlinear oscillator mx′′ + f(x′) + k x = 0 , where m, k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f(x′) = A |x′|α−1x′ with α real, A > 0. We characterize the existence and behaviour of fast orbits, i....

Abstract A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part a vibro-impact unit linear oscillator with an internally colliding small block. This block the secondary being damped oscillator. The mathematical model has been presented in non-dimensional form. analytical studies are restricted to case periodic steady-state motion sy...

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...