【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。更多还原

【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.更多还原