Abstract
In this paper, the Routh method of reduction is extended to the dynamical systems with two kinds of nonstandard Lagrangians on time scales, namely exponential Lagrangians and power-law Lagrangians. Firstly, the definition of cyclic coordinate is given, and the cyclic integrals are obtained by using the Euler–Lagrange equations of the dynamical systems with nonstandard Lagrangians on time scales. Secondly, the Routh equations for the dynamical systems with two kinds of nonstandard Lagrangians on time scales are established. The Routh equations obtained have the same form as the Euler–Lagrange equations before reduction, but the number of equations is reduced. Finally, two examples are given to illustrate the application of the results.
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