广义质量的空间算子代数描述

Depiction of Generalized Mass by Spatial Operator Algebra

应用空间算子代数理论 ,研究机械多体系统广义质量的结构特点 ,研究表明广义质量可初步表示为 :M=HωMω* H* ,并进一步表示为 :M=[I+HωK]D[I+Hω K]* ,其逆矩阵可表示为 :M- 1 =[I-HK]* D- 1 [I-HK]。这种表示与牛顿第二运动定律和欧拉定律相互对应 ,具有简洁的数学表达和明确的物理意义 ,广义质量是正、反向动力学的重要参量 ,是联系旋量力和旋量加速度的桥梁 ,其理论依据源自通过旋量整合的牛顿第二运动定律和欧拉定律 ,即 d2 β/dt2 =M- 1 T′,旋量加速度等于广义质量的逆左乘旋量力。据此可形成对旋量加速度的高效递推算法 ,并为下一时刻的 ω,H,P,D,G,K等参数的正向动力学计算作准备。

The theory of spatial operator algebra (SOA) was firstly used to research the structure characteristics of mass .It is interpreted by the research that generalized mass can be depicted as M=HΦMΦ *H *, and secondly it can be depicted as M=(I+HΦK)D(I+HΦK) *. This kind of depiction has a simple math expression and a clear physical meaning, so generalized mass is the important factor of forward and reward dynamics, and it is the bridge linking rotate force and rotate acceleration ,the theory of which is derived from Newton equation and Eulor equation through rotate vector, just like d 2 β /d t 2=M -1 T′,that means rotate acceleration equals to inversed generalized mass multiplying rotate force;and then a high effective recursive method to compute velocity can be formed by it. Which prepare for the forward dynamic calculations of such factors as Φ,H,P,D,G,K and so on at the next time.