To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms,the determining equations of the Lie symmetry of the system is derived.A conserved quantity of Hojman's type and a Noether's conserved quantity are deduced by the Lie symmetry under some conditions.One example is given to illustrate the application of the result.
This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type.First,the definition and the criterion of the symmetry of the system are given.Secondly,it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity.Finally,an example is shown to illustrate the application of the result.
This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.
