Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system
完整系统Nielsen方程的统一对称性与守恒量

The unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system are studied. On the base of the Nielsen equation, we first give the Noether symmetry, the Lie symmetry and the Mei symmetry for the equation and the conserved quantities deduced from them, then the definition and the criterion for unified symmetry of Nielsen equation are presented, lastly, the Mei conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the result.