conserved quantity

摘要： The purpose of this paper is to study the symmetry of first order Lagrangians and the corresponding conserved quantity. The relation between the Lagrangians and the Birkhoff's functions and the Birkhoff symmetry of Birkhoffian systems are used to obtain the symmetry of first order Lagrangians and the corresponding conserved quantity. Two examples are given to illustrate the application of the result.

摘要： In this paper , a new form conserved quantity of differential equations is presented. The conserved quantity is constructed only based on the general Lie group of transformation vector of the differential equations. The first-order and second-order differential equations are studied, respectively. Two theorems concerning conservedquantities are proved. The relations between these theorems and preious conservation laws are discussed. A condition is given to exclude trivial conserved quantities. Finally, we give two examples to illustrate the application of the results.