Abstract
The Ermakov–Milne–Pinney equation is ubiquitous in many areas of physics that have an explicit time-dependence, including quantum systems with time-dependent Hamiltonian, cosmology, time-dependent harmonic oscillators, accelerator dynamics, etc. The Eliezer and Gray physical interpretation of the Ermakov–Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov–Milne–Pinney equation and associated first integral. The special relativistic extension of the Ray–Reid system and invariant is obtained. General properties of the relativistic Ermakov–Milne–Pinney are analyzed. The conservative case of the relativistic Ermakov–Milne–Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered to be well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov–Milne–Pinney equation has additional nonlinearities, due to the relativistic effects.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Subject
General Earth and Planetary Sciences,General Environmental Science
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献