Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations
Luo Shao-Kai(罗绍凯)a)b)†
a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou 310018, China
Abstract For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables $t$, $q_s $ and $\dot{q}_s $. An example is given to illustrate the application of the results.
Accepted manuscript online:
PACS:
45.20.Jj
(Lagrangian and Hamiltonian mechanics)
Fund: Project supported by the
National Natural Science Foundation of China (Grant Nos 10372053
and 10472040).
Cite this article:
Luo Shao-Kai(罗绍凯) Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 2007 Chinese Physics 16 3182
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