Conserved and piecewise‐conserved Runge vectors for the isotropic harmonic oscillator
作者:
Lawrence H. Buch,
Harry H. Denman,
期刊:
American Journal of Physics
(AIP Available online 1975)
卷期:
Volume 43,
issue 12
页码: 1046-1048
ISSN:0002-9505
年代: 1975
DOI:10.1119/1.10036
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
A procedure for constructing a Runge vector for a particle moving (classically or relativistically) under any central force has been given by Fradkin. Serebrennikov and Shabad have pointed out that such vectors may be piecewise conserved, rather than constants for the entire motion. It is shown herein that, for the classical isotropic harmonic oscillator, the above procedure can lead to a piecewise‐conserved Runge vector as well as to a conserved one (of the same magnitude). We relate this ambiguity to the symmetries of the orbit.
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