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This article is cited in 5 scientific papers (total in 5 papers)
Multiplicative form of the Lagrangian
K. Surawuttinacka, S. Yoo-Kongabc, M. Tanasittikosola a Theoretical and Computational Physics Group, Department of Physics, Faculty of Science,
King Mongkut's University of Technology Thonburi, Thailand
b Theoretical and Computational Science Center, Faculty of Science, King Mongkut's
University of Technology Thonburi, Thailand
c Ratchaburi Campus, King Mongkut's University of Technology Thonburi, Thailan
Abstract:
We obtain an alternative class of Lagrangians in the so-called the multiplicative form for a system with one degree of freedom in the nonrelativistic and the relativistic cases. This new form of the Lagrangian can be regarded as a one-parameter class with the parameter $\lambda$ obtained using an extension of the standard additive form of the Lagrangian because both forms yield the same equation of motion. We note that the multiplicative form of the Lagrangian can be regarded as a generating function for obtaining an infinite hierarchy of Lagrangians that yield the same equation of motion. This nontrivial set of Lagrangians confirms that the Lagrange function is in fact nonunique.
Keywords:
nonuniqueness, multiplicative form, Hamiltonian.
Received: 12.11.2015 Revised: 27.11.2015
Citation:
K. Surawuttinack, S. Yoo-Kong, M. Tanasittikosol, “Multiplicative form of the Lagrangian”, TMF, 189:3 (2016), 335–354; Theoret. and Math. Phys., 189:3 (2016), 1693–1711
Linking options:
https://www.mathnet.ru/eng/tmf9101https://doi.org/10.4213/tmf9101 https://www.mathnet.ru/eng/tmf/v189/i3/p335
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Abstract page: | 276 | Full-text PDF : | 116 | References: | 40 | First page: | 12 |
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