Abstract
Time scale analysis can not only uniformly describe continuous, discrete or quantum dynamics issues, but also deal with complex dynamical processes mixed with them. Therefore, it has both theoretical necessity and prospect in engineering applications to explore symmetry and conservation laws of time scale mechanical systems. In this study, we focus on dynamics modeling and Noether symmetry theory of time-scale nonshifted systems under Lagrangian framework, including nonshifted Lagrangian systems, nonshifted general holonomic systems and nonshifted nonholonomic systems. We present the nonshifted Hamilton principle and extend it to non-conservative systems, from where the nonshifted differential equations of motion are derived. With Noether symmetries for nonshifted constrained mechanical systems defined and their criteria given, we prove Noether’s theorems for time-scale nonshifted systems, respectively. Two examples show the validity of the theorems.
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