Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems
WANG Peng1, FANG Jian-Hui2, WANG Xian-Ming1
1School of Math-Physics and Information Science, Xinjiang Normal University, Urumqi 8300542College of Physics Science and Technology, China University of Petroleum, Dongying 257061
Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems
WANG Peng1, FANG Jian-Hui2, WANG Xian-Ming1
1School of Math-Physics and Information Science, Xinjiang Normal University, Urumqi 8300542College of Physics Science and Technology, China University of Petroleum, Dongying 257061
摘要We study a new symmetric perturbation, i.e. weakly Noether symmetric perturbation (WNSP). The criterion and definition of WNSP and Noether symmetric perturbation (NSP) are given. A theorem between WNSP and adiabatic invariants is established. It is concluded that WNSP is different from NSP, the sufficient condition when WNSP is NSP can be presented, and the former is broader. We apply our results to the planar Kepler problem.
Abstract：We study a new symmetric perturbation, i.e. weakly Noether symmetric perturbation (WNSP). The criterion and definition of WNSP and Noether symmetric perturbation (NSP) are given. A theorem between WNSP and adiabatic invariants is established. It is concluded that WNSP is different from NSP, the sufficient condition when WNSP is NSP can be presented, and the former is broader. We apply our results to the planar Kepler problem.
WANG Peng;FANG Jian-Hui;WANG Xian-Ming. Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems[J]. 中国物理快报, 2009, 26(3): 34501-034501.
WANG Peng, FANG Jian-Hui, WANG Xian-Ming. Discussion on Perturbation to Weak Noether Symmetry and Adiabatic Invariants for Lagrange Systems. Chin. Phys. Lett., 2009, 26(3): 34501-034501.
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2009, Vol. 26 
