The Symmetry And Conserved Quantity For Holonomic Mechanical Systems In Terms Of Quasi-coordinates

Using symmetry to seek the conservation quantity inmoder mathematics and mechanics plays a very importantrole. The main methods of seeking the conserved quantitiesare Noether symmetry, Lie symmetry and the recent yearsraised Mei symmetry and conformal invariance theory.Noether symmetry is a kind of invariance which thehamiton action functional group under the infinitesimaltransformation. Lie symmetry is a kind of invariance whichthe equation under the time and coordinate infinitesimaltransformations. Mei symmetry is a kind of invariance whichthe equations of motion still satisfy the original equationswhich under the infinitesimal transformation.The three kinds of symmetry respectively leads to theCorresponding conserved quantities，which are NoetherSymmetry，Lie symmetry, Mei symmetry.In recent years, the new proposed confomal invariance theoryhave new application in dynamical systems. Robert M L,Mattewdiscuss the Hamiton system for confomal invariance using ageometric method. Galiullin A S and other authors also studied the Brikhoff system confomal invariance, finally leads toNoether conserved quantity. The motion equation with quasiccoordinates is more universal than with the generalizedcoordinates. So the study of symmetry and conserved quantitywith quasic coordinates is more meaningful. The paper mainlystudied the symmetry and conserved quantity with quasicoordinates, obtain the criterion equation, structural equationand the conserved quantitiy.