Classical Canonical Transformations without the Use of Hamilton's Principle
作者:
F. Ansbacher,
期刊:
American Journal of Physics
(AIP Available online 1966)
卷期:
Volume 34,
issue 11
页码: 1020-1024
ISSN:0002-9505
年代: 1966
DOI:10.1119/1.1972417
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
A canonical transformation leading from a Hamiltonian systemΣto anotherΣ*is symmetrical in the sense that the transformation fromΣ*toΣis also canonical. By writing the transformation functions in such a way that the symmetry is exhibited explicitly, i.e., that neitherΣnorΣ*is singled out, one is naturally lead to consider an intermediate coordinate systemSwith 2nindependent coordinates,ncoordinates fromΣ, andnfromΣ*. Working fromSit is then a straightforward matter to derive all the properties of canonical transformations. It is shown that the arbitrariness of the Lagrangian to within the addition of the total time derivative of an arbitrary function of the coordinates and the time follows from Lagrange's equations of motion. It is therefore also possible to derive the generating functions of canonical transformations without an appeal to Hamilton's principle.
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