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arXiv · 1502.03560

On the multiplicative form of the Lagrangian

Kittikun Surawuttinack·Sikarin Yoo-Kong·Monsit Tanasittikosol
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Abstract

An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a 1-parameter: {\lambda} extended class from the standard additive form of the Lagrangian since both yield the same equation of motion. Remarkably, the multiplicative form of the Lagrangian could be treated as a generating function to produce an infinite hierar- chy of Lagrangians which give the same equation of motion. This nontrivial set of Lagrangians confirms that indeed Lagrange function is not unique.

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Kittikun Surawuttinack, Sikarin Yoo-Kong, Monsit Tanasittikosol. 2015-02-12. On the multiplicative form of the Lagrangian. https://doi.org/10.1134/s0040577916120023

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