摘要
针对小干扰力作用下一般的完整保守力学系统对称性的摄动问题，提出了高阶绝热不变量的概念，给出了各阶绝热不变量的形式及存在条件，并将有关结论推广到非保守系统和非完整系统．本文还建立了绝热不变量与对称变换之间的对应关系，证明了线性单自由度Ｈａｍｉｌｔｏｎ系统的绝热不变量Ｈ／ω产生于其关于时间的对称变换．
The perturbation problem of symmetry for holonomic conservative dynamical system under small excitation is discussed. We present the concept of high-order adiabatic invariant,and give the form of the adiabatic invariants and the conditions for their existence. Then these results are genealized to the nonholonomic and nonconservative mechanical systems. The relationship between adiabatic invariant and symmetrical transformation is established. It is proved that adiabatic invariant H/ω for linear Hainiltonion system of one degree of freedom is corresponding to the symmetrical transformation about time.
出处
《湖南大学学报（自然科学版）》
EI
CAS
CSCD
1996年第1期45-50,共6页
Journal of Hunan University:Natural Sciences
基金
国家自然科学基金
机械工业部教育科研基金
