相关论文: Alternative perturbation approaches in classical m…

In this paper we analyze a recent application of perturbation theory by the moment method to a family of two-dimensional anharmonic oscillators. By means of straightforward unitary transformations we show that two of the models studied by…

A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…

We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials.…

Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…

The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.

The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…

A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…

We study the classical and quantum perturbation theory for two non--resonant oscillators coupled by a nonlinear quartic interaction. In particular we analyze the question of quantum corrections to the torus quantization of the classical…

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet--Magnus expansion for periodic systems, the…

A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…

A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…

A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…

The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…

We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustrative examples.

We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a…

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…

This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…

The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…

Orbital motion of a body can be found from Newtonian equation of motion. However, it is useful to express the motion through time derivatives of Keplerian orbital elements, mainly if the motion is perturbed by small perturbing force. The…