时间尺度上非完整力学系统的Noether对称性与守恒量

发布时间：2018-03-22 21:26

本文选题：时间尺度　切入点：非完整系统　出处：《苏州科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文研究了时间尺度上非完整力学系统的Noether理论。分别给出了时间尺度上位形空间中非Chetaev型非完整力学系统、相空间中非Chetaev型非完整力学系统、Nabla变分问题的非完整力学系统以及可控非完整力学的Noether对称性与守恒量。首先,提出时间尺度上位形空间中Hamilton原理,建立了时间尺度上位形空间中非Chetaev非完整力学系统的运动微分方程;基于时间尺度上位形空间中Hamilton作用量在无限小群变换下的不变性,利用时间重新参数法,给出了时间尺度上位形空间中非Chetaev非完整力学系统的Noether等式,并导出相应的守恒量。其次,引进时间尺度上广义动量,依据时间尺度上相空间中Hamilton原理,建立了时间尺度上相空间中非Chetaev非完整力学系统的运动微分方程;基于时间尺度上相空间中Hamilton作用量在无限小群变换下的不变性,利用时间重新参数法,给出了时间尺度上相空间中非Chetaev非完整力学系统的Noether等式,并导出相应的守恒量。再次,根据时间尺度上微积分理论和Delta导数与Nabla导数之间的关系,建立了时间尺度上Nabla导数的非完整Lagrange运动微分方程;根据时间尺度上Nabla变分问题的Hamilton作用量在无限小群变换下的不变性,给出了时间尺度上Nabla变分问题的非完整力学系统的Noether等式,并找到了相应的守恒量。最后,提出在约束条件中加入可控参数,根据时间尺度上Hamilton原理,建立了时间尺度上可控非完整力学系统的运动微分方程;基于时间尺度上Hamilton作用量在无限小群变换下的不变性,利用时间重新参数法,给出了时间尺度上可控非完整力学系统的Noether等式,并导出相应的守恒量。
[Abstract]:In this paper, the Noether theory of nonholonomic mechanical systems on time scale is studied, and the non-#en1# nonholonomic mechanical systems of time scale epistatic space are given respectively. The nonholonomic mechanical system and the Noether symmetry and conserved quantity of controllable nonholonomic mechanics for nonholonomic mechanical systems of Chetaev type in phase space are presented. Firstly, the Hamilton principle in time scale epistatic space is proposed. The differential equation of motion of nonholonomic Chetaev mechanical system in time scale epistatic space is established, based on the invariance of Hamilton action in time scale epistatic space under infinitesimal group transformation, the time reparameter method is used. In this paper, the Noether equation of nonholonomic Chetaev mechanical system in time scale epistatic space is given, and the corresponding conserved quantities are derived. Secondly, the generalized momentum on time scale is introduced, according to the Hamilton principle in phase space on time scale. The motion differential equation of nonholonomic Chetaev mechanical system in phase space on time scale is established, based on the invariance of Hamilton action under infinitesimal group transformation in phase space on time scale, the time reparameter method is used. The Noether equation for nonholonomic Chetaev mechanical systems in phase space on time scale is given, and the corresponding conserved quantities are derived. Thirdly, according to the calculus theory on time scale and the relation between Delta derivative and Nabla derivative, The nonholonomic Lagrange differential equations of motion with Nabla derivatives on time scale are established, and the invariance of the Hamilton action of Nabla variational problem under infinitesimal group transformation on time scale is obtained. In this paper, the Noether equation of nonholonomic mechanical systems for Nabla variational problems on time scale is given, and the corresponding conserved quantities are found. Finally, it is proposed to add controllable parameters to the constraint conditions, according to the Hamilton principle on time scale. The motion differential equation of controllable nonholonomic mechanical system on time scale is established, based on the invariance of Hamilton action under infinitesimal group transformation on time scale, the time reparameter method is used. The Noether equation of controllable nonholonomic mechanical systems on time scale is given and the corresponding conserved quantities are derived.
【学位授予单位】：苏州科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O316

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