非定常完整约束系统的线性映射方法

LINEAR MAPPING METHOD FOR HOLONOMIC RHEONOMIC SYSTEMS

通过一阶线性映射可以从非定常完整约束系统的位形空间映射出一个时空Π,并诱导出时空Π上的附加几何结构(度规和联络),由此可以写出约束系统在时空Π中的运动方程.当一阶线性映射不可积时,时空Π是一个Riemann Cartan空间;当一阶线性映射可积时,时空Π将退化为一个Riemann空间,且此时由这种线性映射方法得到的时空Π中的运动方程等价于用广义坐标表示的约束系统的Lagrange方程.

Through first order linear mapping,a space timeΠwas mapped out from the configuration space of a system with a holonomic rheonomic constraint.The geometric properties(metric and connection)of the space timeΠwere induced,and the equations of motion of the constrained system in the space timeΠwere obtained.When the first order linear mapping is not integrable,the space timeΠis a Riemann Cartan space.When the first order linear mapping is integrable,the space timeΠdegenerates into a Riemann space.In the latter case,the equations of motion of the holonomic rheonomic system in the space timeΠis equivalent to the Lagrange equa tions described with generalized coordinates.