Variational symmetries in the Hamiltonian formalism
DOI:
https://doi.org/10.31349/RevMexFis.71.010701Keywords:
Symmetries, Hamiltonian formalismAbstract
We consider the effect on the Hamilton equations of an arbitrary coordinate transformation in the extended configuration space, $q_{i}' = q_{i}'(q_{j}, t)$, $t' = t'(q_{j}, t)$ (which may not be canonical) and we show that when the Hamiltonian is invariant under a one-parameter family of these transformations, there is an associated nontrivial constant of motion.
References
M. V. Berry and P. Shukla, Classical dynamics with curl forces, and motion driven by time-dependent flux, J. Phys. A: Math. Theor. 45 (2012) 305201. https://doi.org/10.1088/1751-8113/45/30/305201
G. F. Torres del Castillo, C. Andrade Mirón, and R.I. Bravo Rojas, Variational symmetries of Lagrangians, Rev. Mex. Fís. E 59 (2013) 140
G. F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018). https://doi.org/10.1007/978-3-319-95225-3
G. F. Torres del Castillo, Relating the free particle with the harmonic oscillator, Rev. Mex. Fís. (to appear)
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, N.J., 1992), Chap. 4.
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