Xia Li-Li

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The deflnition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and su‐cient condition that the conformal invariance would be the Lie symmetry of the system under the inflnitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems

This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry under the infinitesimal single-parameter transformation group. The generalized Hojman conserved quantities from the conformal invariance of the system are given. An example is given to illustrate the application of the result.

A Field Integration Method for a Nonholonomic Mechanical System of Non-Chetaev's Type

A field integration method for a nonholonomic mechanical system of non-Chetaevs type is studied. The differential equations of the motion of the system are established. The solution of the corresponding holonomic system for the nonholonomic system is obtained by the field method. The restriction of nonholonomic constrained to initial conditions is added and the solution of the nonholonomic mechanical system of non-Chetaevs type is provided. An example is presented to illustrate the application of the results.

Generalized Mei Conserved Quantity of Mei Symmetry for Mechanico-electrical Systems with Nonholonomic Controllable Constraints

On the basis of the total time derivative along the trajectory, we study the generalized Mei conserved quantity of Mei symmetry for mechanico-electrical systems with nonholonomic controllable constraints. Firstly, the definition and criterion of Mei symmetry for mechanico-electrical systems with nonholonomic controllable constraints are presented. Secondly, a coordination function is introduced, and the conditions of existence of generalized Mei conserved quantity as well as the forms are proposed. Lastly, an example is given to illustrate the application of the results.

Poisson Theory and Inverse Problem in a Controllable Mechanical System

The Poisson theory and inverse problem are studied in a controllable mechanical system. Equations of motion of the controllable mechanical system in phase space are given. Poissons integral theory of the system is established. The potential force field is constructed by solving the inverse problem in a controllable mechanical system. Finally, an example is given to illustrate the application of the results.

Symmetry of Lagrangians of Nonholonomic Controllable Mechanical Systems

Symmetry of Lagrangians of nonholonomic controllable mechanical systems is studied. The definition and criterion of the symmetry of the system are presented. Under the condition that there exists a conserved quantity, the form of the conserved quantity is provided. An example is presented to illustrate the application of the results.

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechanical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is given to illustrate the application of the results.

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.

Weak Noether symmetry for a nonholonomic controllable mechanical system

This paper discusses the weak Noether symmetry for a nonholonomic controllable mechanical system of Chetaev type, and presents expressions of three kinds of conserved quantities obtained by using weak Noether symmetry. Finally, the application of these new results is illustrated by an example.