变质量完整系统的Herglotz型微分变分原理与守恒律

Herglotz type differential variational principles and conservation laws forholonomic systems with variable mass

为了进一步探究变质量力学系统的Herglotz变分问题与其守恒律的关系,论文基于Herglotz微分变分原理构建变质量完整系统的守恒律。给出变质量完整系统的Herglotz型广义变分原理,导出变质量完整系统的Herglotz型微分变分原理。引进空间和时间的生成元,建立Herglotz型微分变分原理不变性条件的变换,并基于该原理构建变质量完整系统的Herglotz型守恒量及其逆定理。最后,给出两个算例以说明结果的应用。

In order to explore the relationship between the Herglotz variational problem of variable mass system and its conservation laws,this paper constructed the conservation laws of holonomic system with variable mass based on Herglotz differential variational principles.The generalized variational principles of Herglotz type for mechanical system with variable mass were given,and the differential variational principles of Herglotz type for holonomic system with variable mass were derived.The transformation of invariance condition of Herglotz type differential variational principles was established by introducing space and time generating functions.Based on these principles,Herglotz type conservation theorem and its inverse for variable mass holonomic system have been constructed.Finally,two examples were given to illustrate the application.