In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Suf...Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.展开更多
针对车式移动机器人的编队问题,提出一种多机器人动态协调控制算法.首先利用领航机器人和跟随机器人期望位姿参数生成虚拟机器人,建立跟随机器人对虚拟机器人轨迹跟踪系统模型.然后将机器人运动学模型转化为链式标准形,运用反步法,逐步...针对车式移动机器人的编队问题,提出一种多机器人动态协调控制算法.首先利用领航机器人和跟随机器人期望位姿参数生成虚拟机器人,建立跟随机器人对虚拟机器人轨迹跟踪系统模型.然后将机器人运动学模型转化为链式标准形,运用反步法,逐步构造轨迹跟踪系统的李亚普诺夫函数,并通过使该函数负定,得到跟随机器人的轨迹跟踪控制器,实现了车式移动机器人的编队控制.最后在Microsoft Robotics Developer Studio 4(MRDS4)中搭建3D仿真平台,设计了3组实验,验证了所提方法的有效性.展开更多
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10672143 and 10572021
文摘Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.
文摘针对车式移动机器人的编队问题,提出一种多机器人动态协调控制算法.首先利用领航机器人和跟随机器人期望位姿参数生成虚拟机器人,建立跟随机器人对虚拟机器人轨迹跟踪系统模型.然后将机器人运动学模型转化为链式标准形,运用反步法,逐步构造轨迹跟踪系统的李亚普诺夫函数,并通过使该函数负定,得到跟随机器人的轨迹跟踪控制器,实现了车式移动机器人的编队控制.最后在Microsoft Robotics Developer Studio 4(MRDS4)中搭建3D仿真平台,设计了3组实验,验证了所提方法的有效性.
