基于李群李代数的车用稳定平台加速度分析方法

The Analysis Method of Vehicle Stability Platform Acceleration Based on Lie Groups and Lie Algebras

基于李群李代数方法,通过对刚体运动旋量即刚体速度求时间导数得到了刚体加速度,证明了它们是李代数的元素,并验证了李群对刚体加速度旋量的伴随作用;通过数学公式推导揭示了刚体加速度的物理意义及其与传统描述的区别;在此基础上分析了各刚体之间的运动关系,从而给出了多刚体系统刚体加速度伴随变换表达式,为直接应用六维矢量表示分析并联式车载稳定平台的加速度和动力学提供了一种有效途径。

Based on Lie Groups and Lie Algebras method, this paper obtained the rigid body acceleration through rigid body motion spinor, that is, the rigid body speed strived for time derivative, it also proved that they were elements of Lie Algebras and verified the adjoint effect of Lie Groups on rigid body acceleration spinor. It revealed the physical meaning of the rigid body acceleration and its difference with the traditional description through the mathematic formulation derivation. On this basis, it also analyzed the movement relationship between the rigid body, thus it gave the adjoint transformation expression of the multi-rigid-body system rigid body acceleration, which provided an effective way for analyzing parallel-type vehicle stability platform acceleration and dynamics with the direct application of six dimensional vector.