用微元法建立单刚体动力学的虚加速度原理和虚力原理

Derivation of Virtual Acceleration Principle and Virtual Force Principle for Single Rigid Body Dynamics by Infinitesimal Element Method

本文首先从刚体动力学方程出发,利用变积法推得其虚加速度原理和虚力原理,然后用微元法思想由质点系动力学的虚加速度原理、虚力原理推得刚体动力学的虚加速度原理与虚力原理,并对两种方法本身进行了比较。由于本文的推导方法是从连续介质力学的观点进行的,故这种方法对进一步建立单柔体、多柔体动力学的虚加速度原理和虚力原理具有重要应用价值,进而对现在热点之一的柔性飞行器动力学的研究有潜在的意义。

Starting from the governing equations of rigid body dynamics,the virtual acceleration principle and virtual force principle of rigid body dynamics are derived in this paper by using variational integral method.Then the two principles of rigid body dynamics are derived again from the virtual acceleration principle and virtual force principle of system of particles using the infinitesimal element method and a comparison of the two ways of derivation is made.The derivations in this paper are performed from the view of continuum mechanics,thus are valuable in the application for the establishment of virtual acceleration principle and virtual force principle of single flexible body dynamics and multi-flexible body dynamics,and consequently are of certain significance to the research of flexible aircraft dynamics which is currently one of the hot spots in research.