Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differenti...Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The di...Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman's conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.展开更多
A form invariance of Raitzin's canonical equations of relativistie mechanical system is studied. First, the Raitzin's canonical equations of the system are established. Next, the definition and criterion of th...A form invariance of Raitzin's canonical equations of relativistie mechanical system is studied. First, the Raitzin's canonical equations of the system are established. Next, the definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. Finally,the relation between the form invariance and the conserved quantity of the system is obtained and an example is given to illustrate the application of the result.展开更多
The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetri...The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.展开更多
文摘Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
文摘Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman's conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.
文摘A form invariance of Raitzin's canonical equations of relativistie mechanical system is studied. First, the Raitzin's canonical equations of the system are established. Next, the definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. Finally,the relation between the form invariance and the conserved quantity of the system is obtained and an example is given to illustrate the application of the result.
文摘The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.
