This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems...This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11072218 and 11272287)the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)(No.IRT13097)
文摘This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conserva-tive and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this re-lation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.
