Generalized Lagrangian and conservation law for the damped harmonic oscillator
作者:
Leon Y. Bahar,
Harry G. Kwatny,
期刊:
American Journal of Physics
(AIP Available online 1981)
卷期:
Volume 49,
issue 11
页码: 1062-1065
ISSN:0002-9505
年代: 1981
DOI:10.1119/1.12644
出版商: American Association of Physics Teachers
关键词: CONSERVATION LAWS;TIME DEPENDENCE;LAGRANGIAN FUNCTION;EQUATIONS OF MOTION;HARMONIC OSCILLATORS;DAMPING
数据来源: AIP
摘要:
An explicit construction of the time‐dependent Lagrangian for a damped harmonic oscillator is given. The connection between this Lagrangian with the time‐independent one developed by Morse and Feshbach is established. Various methods of deriving a first integral for the equation of motion are given. It is shown that the results developed in this paper by direct means are in agreement with those obtained through the use of group‐theoretic methods, such as invariance principles and Noether’s theorem, which are mathematically more advanced approaches.
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