摘要
研究了具有单面约束的Birkhoff系统在小扰动作用下对称性的摄动与不变量之间的关系 .首先 ,建立了系统的运动微分方程 ,给出了系统的精确不变量 ;其次 ,基于力学系统的高阶绝热不变量的概念 ,得到了系统的绝热不变量存在的条件及其形式 ;最后 。
The relation between the invariant and the perturbation to symmetries of Birkhoffian systems with unilateral constraints under the action of small disturbance is studied. First, the differential equations of motion of the systems are established, and the exact invariant of the systems is obtained. Next, based on the concept of high-order adiabatic invariant of mechanical systems, the form of the adiabatic invariant and the conditions for their existence are given; and finally, an example is given to illustrate the application of the results.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2002年第8期1666-1670,共5页
Acta Physica Sinica
基金
国家自然科学基金 (批准号 :19972 0 10 )
江苏省青蓝工程基金资助的课题~~
关键词
分析力学
单面约束
BIRKHOFF系统
对称性
摄动
绝热不变量
analytical mechanics
unilateral constraint
Birkhoffian system
symmetry
perturbation
adiabatic invariant