Noether Lie Symmetry Research Articles

Noether-Lie symmetry and conserved quantities of Nielsen equations for a singular variable mass nonholonomic system with unilateral constraints

Under the infinitesimal transformations of Lie group, Noether-Lie symmetry of Nielsen equations for a singular variable mass nonholonomic system with unilateral constraints is studied. Differential equations of motion for Nielsen equations of the system are established. The definition, criteria and propositions for Nielsen equations of the system are given. Noether conserved quantity as well as generalized Hojman quantity is obtained. An example is given to illustrate the application of the results.

Noether-Lie symmetry and conserved quantities of the Rosenberg problem

The Noether-Lie symmetry and conserved quantities of the Rosenberg problem are studied. From the study of the Rosenberg problem,the Noether symmetry and the Lie symmetry for the equation are obtained, thereby the conserved quantities are deduced. Then the definition and the criterion for Noether-Lie symmetry of the Rosenberg problem are derived. Finally,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry.

Perturbation to Noether–Lie Symmetry and Adiabatic Invariants for Mechanical Systems in Phase Space

Based on the concept of adiabatic invariant, the perturbation to Noether–Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied. The criterion of the Noether–Lie symmetry for the perturbed system is given, and the definition of the perturbation to Noether–Lie symmetry for the system under the action of small disturbance is presented. Meanwhile, the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained.

Noether–Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether–Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether–Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether–Lie symmetry are obtained. An example is given to illustrate the application of the results.

Noether–Lie symmetry and conserved quantities of mechanical system in phase space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether–Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether–Lie symmetry of the system are obtained. The Noether–Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.

Noether-Lie symmetry of non-holonomic mechanical system

In this paper, a new symmetry, i.e., Noether-Lie symmetry and its conserved quantities of the non-holonomic mechanical system is studied. The definition and the criterion of the Noether-Lie symmetry for the system are given. A theorem asserting that the Noether-Lie symmetry for the system leads to both the Noether conserved quantity and the general Hojman conserved quantity is presented. An example is given to illustrate the application of the result. The Hojman conserved quantity of the system is a special case of the general Hojman conserved quantity obtained in this paper.