| 包含伺服约束的非完整系统的对称性摄动与绝热不变量 |
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| 引用本文： | 陈向炜,梅凤翔,等.包含伺服约束的非完整系统的对称性摄动与绝热不变量[J].上海力学,2001,22(2):204-209. |
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| 作者姓名： | 陈向炜 梅凤翔 |
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| 作者单位： | [1]北京理工大学应用力学系，北京100081；商丘师范学院物理系，河南商丘476000 [2]北京理工大学应用力学系，北京10 |
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| 基金项目： | 国家自然科学基金(19972010);河南省教委科研基金(2000130003) |
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| 摘 要： | 建立包含伺服约束系统的运动微分方程，基于包含伺服约束系统对称性与不变量理论研究包含伺服约束系统的对称性摄动与绝热不变量 问题，提出了包含伺服约束系统的高阶绝热不变量概念，证明了精确不变量与绝热不变量存在的条件及形式，并举例说明结果的应用。
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| 关 键 词： | 包含伺服约束系统 对称性 摄动 绝热不变量 |
| 修稿时间： | 2000年4月10日 |
Perturbation to Symmetries and Adiabatic Invariant of Nonholonomic Systems with Servoconstraints |
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| CHEN Xiang-wei,MEI Feng-xiang.Perturbation to Symmetries and Adiabatic Invariant of Nonholonomic Systems with Servoconstraints[J].Chinese Quarterly Mechanics,2001,22(2):204-209. |
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| Authors: | CHEN Xiang-wei MEI Feng-xiang |
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| Abstract: | In this paper, the differential equations of motion of nonholonomic systems with servoconstraints were constructed. Based on the theory of symmetries and conserved quantities of nonholonomic systems with servoconstraints, the perturbation to the symmetries and adiabatic invariant of nonholonomic systems with servoconstraints were discussed. First, the concept of high-order adiabatic invariant of nonholonomic systems with servoconstraints was proposed. Then, the conditions for existence of the exact invariant and adiabatic invariant were proved, and their forms were given. Finally, an example is presented to illustrate these results. |
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| Keywords: | nonholonomic systems with servoconstraints symmetry perturbation adiabatic invariant |
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