A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

• 来源期刊: 中国物理（英文版）
• 关键词: generalized classical mechanics adiabatic invariant Lie symmetry perturbation
• 年，卷（期）: 2006,（9）
• 页码范围: 1935-1940
• 页数: 6页
• 语种: 英文

摘要

The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.