Li Ren-Jie

Integrating factors and conservation theorems of constrained Birkhoffian systems

In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.

Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass nonholonomic nonconservative systems. First, we give the definition of integrating factors and we study in detail the necessary conditions for the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem for Hamiltons canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally, we give an example to illustrate the application of the results.

Integrating Factors and Conservation Theorems of Nonholonomic Dynamical System of Relative Motion

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

Non-Noether Conserved Quantity for Relativistic Nonholonomic System with Variable Mass

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.

Hojman's conservation theorems for generalized Raitzin canonical equations of motion

Using the Lie symmetry under infinitesimal transformations in which the time is not variable, Hojmans conservation theorems for Raitzins canonical equations of motion in generalized classical mechanics are studied. The generalized Raitzins canonical equations of motion are established. The determining equations of Lie symmetry under infinitesimal transformations are given. The Hojman conservation theorems of the system are established. Finally, an example is also presented to illustrate the application of the result.

Exact invariants and adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system

The exact invariants and the adiabatic invariants of Raitzins 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.

Form invariance of Raitzin's canonical equations of a nonholonomic mechanical system

A form invariance of Raitzins canonical equations of a nonholonomic mechanical system is studied. The Raitzin canonical equations of the system are established. The definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. The relation between the form invariance and the conserved quantity of the system is obtained and an example is also given to illustrate the application of the result.

Non-Noether Conserved Quantity of Nonholonomic System Having Variable Mass and Unilateral Constraints

Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the non-Noether 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 Hojmans conservation theorem of the system is established. Finally, we give an example to illustrate the application of the result.

Non-Noether symmetrical conserved quantity for nonholonomic Vacco dynamical systems with variable mass

Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.

Form invariance and conserved quantities of Nielsen equations of relativistic variable mass nonholonomic systems

In this paper, the definition and criterion of the form invariance of Nielsen equations for relativistic variable mass nonholonomic systems are given. The relation between the form invariance and the Noether symmetry is studied. Finally, we give an example to illustrate the application of the result.