Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

2013 ◽  
Vol 22 (3) ◽  
pp. 030201 ◽  
Author(s):  
Gang-Ling Zhao ◽  
Li-Qun Chen ◽  
Jing-Li Fu ◽  
Fang-Yu Hong
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Symmetry And Conservation Laws ◽  
Mei Symmetry ◽  
Nonholonomic Dynamical Systems

scholarly journals Mei Symmetry and Conservation Laws for Time-Scale Nonshifted Hamilton Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yi Zhang
Keyword(s):  
Phase Space ◽  
Conservation Laws ◽  
Time Scale ◽  
Symmetry And Conservation Laws ◽  
Dynamic Equations ◽  
Constrained Mechanical Systems ◽  
Hamilton Principle ◽  
Hamilton Equations ◽  
Mei Symmetry ◽  
Case Based

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.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

scholarly journals Symmetry and conservation laws in non-holonomic mechanics

2021 ◽  
Vol 62 (5) ◽  
pp. 052901
Author(s):  
Enrico Massa ◽  
Enrico Pagani
Keyword(s):  
Conservation Laws ◽  
Symmetry And Conservation Laws

Lagrangian Mechanics

2019 ◽  
pp. 53-82
Author(s):  
David D. Nolte
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Euler Equations ◽  
Virial Theorem ◽  
Variational Calculus ◽  
Mechanical Action ◽  
Lagrange Equations ◽  
Time Average ◽  
The Difference ◽  
Kinetic And Potential Energies

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and potential energies, which is also the time average of the Lagrangian. Once a Lagrangian has been defined for a system, the Euler equations of variational calculus lead to the Euler–Lagrange equations of dynamics. This chapter explores applications of Lagrangians and the use of Lagrange’s undetermined multipliers. Conservation laws, central forces, and the virial theorem are developed and explained.

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