The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the ...The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system 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 a mechanical system under the action of a small perturbation, the forms 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
In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonica...In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.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
基金Project supported by the Heilongjiang Natural Science Foundation of China （Grant No 9507）.
文摘The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system 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 a mechanical system under the action of a small perturbation, the forms 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.
文摘In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.
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.
