Qiao Yong-Fen

GIBBS-APPELL'S EQUATIONS OF VARIABLE MASS NONLINEAR NONHOLONOMIC MECHANICAL SYSTEMS

In this paper, the Gibbs-Appells equations of motion are extended to the most general variable mass nonholonomic mechanical systems. Then the Gibbs-Appells equations of motion in terms of generalized coordinates or quasi-coordinates and an integral variational principle of variable mass nonlinear nonholonomic mechanical systems are obtained. Finally, an example is given.

Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

In this paper, we present a general approach to the construction of conservation laws for generalized classical dynamical systems. Firstly, we give the definition of integrating factors and, secondly, we study in detail the necessary conditions for the existence of conserved quantities. Then we establish the conservation theorem and its inverse for the Hamiltons canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics. Finally, we give an example to illustrate the application of the results.

Kane's equations for percussion motion of variable mass nonholonomic mechanical systems

In this paper, the Kanes equations for the Rouths form of variable mass nonholonomic systems are established, and the Kanes equations for percussion motion of variable mass holonomic and nonholonomic systems are deduced from them. Secondly, the equivalence to Lagranges equations for percussion motion and Kanes equations is obtained, and the application of the new equation is illustrated by an example.

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.

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems. Firstly, we give the definition of integrating factors for the differential equations of motion of a mechanical system. Next, the necessary conditions for the existence of the conserved quantities are studied in detail. Then, we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system. Finally, an example is given to illustrate the application of the result.

Integrating Factors and Conservation Theorems for the Nonholonomic Singular Lagrange System

We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.

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.

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and 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.