Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An exa...Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.展开更多
The new types of conserved quantities,which are directly induced by Lie symmetry of nonholonomicmechanical systems in phase space,are studied.Firstly,the criterion of the weak Lie symmetry and the strong Liesymmetry a...The new types of conserved quantities,which are directly induced by Lie symmetry of nonholonomicmechanical systems in phase space,are studied.Firstly,the criterion of the weak Lie symmetry and the strong Liesymmetry are given.Secondly,the conditions of existence of the new type of conserved quantities induced by the weakLie symmetry and the strong Lie symmetry directly are obtained,and their form is presented.Finally,an Appell-Hamelexample is discussed to further illustrate the applications of the results.展开更多
The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the inva...The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.展开更多
The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitesimal transformations' generators and by using the invariance of ...The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitesimal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational relativistic mechanical systems are established. The structure equations and the forms of conserved quantities are obtained. An example to illustrate the application of the results is given.展开更多
基金Sponsored by the National Natural Science Foundation of China(10572021)
文摘Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.
基金Supported by the Graduate Students' Innovative Foundation of China University of Petroleum (East China) under Grant No.S2009-19
文摘The new types of conserved quantities,which are directly induced by Lie symmetry of nonholonomicmechanical systems in phase space,are studied.Firstly,the criterion of the weak Lie symmetry and the strong Liesymmetry are given.Secondly,the conditions of existence of the new type of conserved quantities induced by the weakLie symmetry and the strong Lie symmetry directly are obtained,and their form is presented.Finally,an Appell-Hamelexample is discussed to further illustrate the applications of the results.
文摘The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.
文摘The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitesimal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational relativistic mechanical systems are established. The structure equations and the forms of conserved quantities are obtained. An example to illustrate the application of the results is given.
