Showing papers on "Multiple-scale analysis published in 1982"
TL;DR: In this article, the authors have provided most satisfactory approximations for the distribution of sums of independent and correlated, non-Gaussian basic variables and the reliability of a portal frame.
37 citations
TL;DR: In this paper, a method for analyzing multidegree-of-freedom systems having a repeated natural frequency subjected to a parametric excitation is presented, where the analysis is based on the method of multiple scales.
26 citations
TL;DR: In this paper, a new form for describing interacting relativistic classical particles with invariant world-lines is presented, in contrast to the use of independent particle variables or of "centre of mass" and relative co-ordinates previously considered in the literature.
Abstract: A new form for describing interacting relativistic classical particles with invariant world-lines is presented. In contrast to the use of independent particle variables or of «centre of mass» and relative co-ordinates previously considered in the literature, we introduce a Lorentz matrix and an associated conjugate four-dimensional angular momentum as collective variables; these are supplemented with a suitable number of internal variables. The methods of constrained Hamiltonian dynamics are used to ensure that the number of independent degrees of freedom corresponds precisely to that for a system of a given number of particles. Independent particle variables can be defined in the formalism, and interactions included. The eleventh-generator form for relativistic Hamiltonian dynamics is essential to make relativistic invariance, invariant world-lines and interaction compatible with one another.
8 citations
TL;DR: In this paper, a dynamical system which is built up by the interconnection of non-linear subsystems with weak and strong coupling is analyzed, and the perturbation results are found to be in good agreement with those obtained by numerically integrating the coupled system.
Abstract: The method of multiple scales is used to determine the response of a coupled non linear system. A dynamical system which is built up by the interconnection of non-linear subsystems with weak and strong coupling is analysed. The perturbation results are found to be in good agreement with those obtained by numerically integrating the coupled system.
5 citations
01 Jan 1982
TL;DR: In this article, the classical dam problem is used to illustrate a new approach based on the interchange of the dependent variable and one space variable, and the interchange method is extended to solve an axially symmetrical dam problem.
Abstract: Methods of solving free boundary problems are classified as (i) analytic; (ii) front tracking or iterating; (iii) fixed physical domain. The classical dam problem is used to illustrate a new approach based on the interchange of the dependent variable and one space variable. This is a special case of a curvilinear transformation such that in the transformed plane the free boundary becomes a known line. The position of the free boundary is known. Successive stages in a single, iterative process improve both the position of the separation point and the solution of the transformed equation of fluid flow. The interchange method is extended to solve an axially symmetrical dam problem. The method is used successfully to handle a three dimensional problem.