Abstract Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.
Received: 25 October 2005
Revised: 01 November 2005
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311010900).
Cite this article:
Chen Xiang-Wei (陈向炜), Liu Cui-Mei (刘翠梅), Li Yan-Min (李彦敏) Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations 2006 Chinese Physics 15 470
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
