Two Lagrangian formulations for describing the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalizations which enjoy l-conformal Newton-Hooke symmetry. It is shown that dynamics of generalized systems corresponds to Pais-Uhlenbeck a particular choice its frequencies.

In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical tr...

Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation likelihood. We calculate analytic state space for damped simple harmonic oscillator and Mat\'ern 1/2, 3/2 5/2 processes.

The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

We demonstrate complete all-optical and phase-stable control of the linear optical polarization and the nonlinear coherent response (third-harmonic generation) of a hybrid nanoplasmonic-photonic system. A few tens of femtoseconds after the excitation, we turn the response on and off at any given point in time and probe its temporal evolution throughout the control process with a three-pulse non...

The quantum theory of a damped harmonic oscillator has been continuously studied since 1939. For quantization, an oscillation usually uses reservoir that includes number finite and discrete oscillators. However, set oscillators is unable to study the Ohmic damping (damping proportional velocity). In this research, continuous used investigate damping. Using continuum instead will enrich results ...