Abstract
The Mei symmetry and conservation laws for time-scale nonshifted Hamilton equations are explored, and the Mei symmetry theorem is presented and proved. Firstly, the time-scale Hamilton principle is established and extended to the nonconservative case. Based on the Hamilton principles, the dynamic equations of time-scale nonshifted constrained mechanical systems are derived. Secondly, for the time-scale nonshifted Hamilton equations, the definitions of Mei symmetry and their criterion equations are given. Thirdly, Mei symmetry theorems are proved, and the Mei-type conservation laws in time-scale phase space are driven. Two examples show the validity of the results.
Highlights
The symmetry property of dynamic systems is the invariance of some physical quantity to the infinitesimal transformations of a group in mathematical form and can be expressed as a conservation law in physics [1,2,3,4,5]
The classical symmetries we are familiar with include Noether symmetry and Lie symmetry
Compared with Noether or Lie symmetry, Mei symmetry is a new kind of symmetry, and it refers to the invariance that the dynamic functions after infinitesimal transformation still make the dynamic equations hold
Summary
The symmetry property of dynamic systems is the invariance of some physical quantity to the infinitesimal transformations of a group in mathematical form and can be expressed as a conservation law in physics [1,2,3,4,5]. The Noether symmetry is the invariance of the action functional under the infinitesimal transformations of a group, and physically, it is the Noether conservation laws [4, 5]. Compared with Noether or Lie symmetry, Mei symmetry is a new kind of symmetry, and it refers to the invariance that the dynamic functions after infinitesimal transformation still make the dynamic equations hold. The time-scale Mei symmetry is different from Noether or Lie symmetry on time scales It is a new symmetry under the infinitesimal transformations of a group. There have been many research studies on Noether or Lie symmetry on time scales, the research on time-scale nonshifted Mei symmetry has not been reported
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