Direct use of variational principles as an approximation technique in classical mechanics
作者:
C. G. Gray,
G. Karl,
V. A. Novikov,
期刊:
American Journal of Physics
(AIP Available online 1996)
卷期:
Volume 64,
issue 9
页码: 1177-1184
ISSN:0002-9505
年代: 1996
DOI:10.1119/1.18340
出版商: American Association of Physics Teachers
关键词: CLASSICAL MECHANICS;VARIATIONAL METHODS;TRAJECTORIES;RITZ METHOD;HAMILTONIAN FUNCTION;PHASE SPACE;ACTION INTEGRAL;02.;03.20;03.65
数据来源: AIP
摘要:
The Hamilton least action principle, a reformulated Maupertuis least action principle, and their reciprocals, are shown to be useful as direct methods for approximate solutions of dynamics problems. We discuss applications to trajectories of all types, i.e., periodic, quasiperiodic, chaotic, scattering, and arbitrary segments of arbitrary trajectories. The analogy with the standard technique used in quantum mechanics is very striking, especially in one of the reformulations (extremization of the mean energy), and in the calculational procedure (Rayleigh–Ritz type).
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