Xie Jia-Fang

Structure equation and Mei conserved quantity for Mei symmetry of Appell equation

This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.

Symmetry and Hojman Conserved Quantity of Tzénoff Equations for Unilateral Holonomic System

Symmetry of Tzenoff equations for unilateral holonomic system under the infinitesimal transformations of groups is investigated. Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzenoff equations are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the system above through special Lie symmetry and Lie symmetry in the condition of special Mei symmetry respectively is obtained.

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.

A symmetry and a conserved quantity for the Birkhoff system

A symmetry and a conserved quantity of the Birkhoff system are studied. The symmetry is called the Birkhoff symmetry. Its definition and criterion are given in this paper. A conserved quantity can be deduced by using the symmetry. An example is given to illustrate the application of the result.

Weakly Noether Symmetry for Nonholonomic Systems of Chetaev's Type

In the paper [J. of Beijing Institute of Technology 26 (2006) 285] the authors provided the definition of weakly Noether symmetry. We now discuss the weakly Noether symmetry for non-holonomic system of Chetaevs type, and present expressions of three kinds of conserved quantities by weakly Noether symmetry. Finally, the application of this new result is shown by a practical example.

Stability of Motion of a Nonholonomic System

Perturbation differential equations of motion of a general nonholonomic system subjected to the ideal nonholonomic constraints of Chetaevs type are established, and the equation of variation of energy is deduced by using the perturbation equations of the system. A criterion of the stability is obtained and an example is given to illustrate the application of the result.

Mei Symmetry and Conserved Quantity of Tzenoff Equations for Nonholonomic Systems of Non-Chetaev＇s Type

Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaevs type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.

Weak Noether Symmetry and non-Noether Conserved Quantities for General Holonomic Systems

A new kind of weak Noether symmetry for a general holonomic system is defined in such a way that the methods to construct Hojman conserved quantity and new-type conserved quantity are given. It turns out that we introduce a new approach to look for the conserved laws. Two examples are presented.

A New Conserved Quantity Corresponding to Mei Symmetry of Tzénoff Equations for Nonholonomic Systems

A new conserved quantity is investigated by utilizing the definition and discriminant equation of Mei symmetry of Tzenoff equations for nonholonomic systems. In addition, the expression of this conserved quantity, and the determining condition induced new conserved quantity are also presented.

Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems

This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not variable, its criterion is given and a method of how to seek the Hojman conserved quantity is presented. A Hojman conserved quantity can be found by using the special weak Noether symmetry.