单面完整约束系统的Lutzky守恒量

Lutzky conserved quantities for systems with unilateral holonomic constraints

研究了单面完整约束系统的对称性与守恒量。建立了系统的运动微分方程,在时间和空间的点对称变换下,给出了系统的Lie对称性的定义,得到了由单面完整约束力学系统的Lie对称性直接导致的一类新守恒量———Lutzky守恒量,作为特例,给出了有多余坐标系统、非保守系统、Lagrange系统的Lutzky守恒量,并举例说明了该研究结果的应用。

The symmetries and conserved quantities for the systems with unilateral holonomic constraints were studied. The differential equations of motion of the systems were established. Under the point symmetric transformations of the coordinates and time, the definition of Lie symmetry of the system was given, and a new type of conserved quantities called Lutzky conserved quantities, which is directly deduced from Lie symmetries of the system, was obtained. As special cases, the Lutzky conserved quantities for the system with remainder coordinates, the non-conservative system and the Lagrange system, were given. An example was given to illustrate the application of the results.