Abstract
The Noether symmetry and the conserved quantity on time scales in event space are studied in this paper. Firstly, the Lagrangian of parameter forms on time scales in event space are established. The Euler-Lagrange equations and the second Euler-Lagrange equations of variational calculus on time scales in event space are established. Secondly, based upon the invariance of the Hamilton action on time scales in event space under the infinitesimal transformations of a group, the Noether symmetry and the conserved quantity on time scales in event space are established. Finally, an example is given to illustrate the method and results.
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Foundation item: Supported by the National Natural Science Foundation of China (11572212 and 11272227), the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province (KYZZ15_0349) and the Innovation Program of USTS (SKCX15_061)
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Shi, Y., Zhang, Y. Noether Theorem on Time Scales for Lagrangian Systems in Event Space. Wuhan Univ. J. Nat. Sci. 24, 295–304 (2019). https://doi.org/10.1007/s11859-019-1400-z
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DOI: https://doi.org/10.1007/s11859-019-1400-z