并联式六维加速度传感器的哈密顿动力学研究

Research on Hamiltonian Dynamics of Parallel Type Six-axis Accelerometer

针对六维加速度传感器在解耦难度与结构复杂度之间存在矛盾的现状,通过Legende变换,并用四元数来描述旋转运动,建立并联式六维加速度传感器的哈密顿约束正则方程。依据四元数的性质,在相空间内推导出系统哈密顿变量之间隐含的正交关系式,并据此给出一种求解微分代数方程的显式递推算法。通过构建系统内的固有约束关系并求解相容线性方程组的最小范数解,对动力学方程的计算误差进行修正。通过仿真和试验对系统的动力学模型及其算法进行验证,结果相一致,且计算效率较高。研究表明:应用相空间内的哈密顿动力学理论,可以实现并联式六维加速度传感器这类多体系统在一般工作环境下的动力学解耦。

According to the present situation of six-axis accelerometer that difficulty of decoupling and complexity of configuration are contrary, constrained Hamilton canonical equations of parallel type six-axis aecelerometer are derived by transforming of Legende and using quatemions to describe wheel. According to the character of quaternions, implicit orthogonality between Hamiltonian variables of the system is derived in phase-space, and then a new explicit recursive algorithm to solve differential algebraic equations is put forward. Calculating errors of dynamic equations can be modified by constructing inherent constraint relations of the system and solving minimum norm solution of consistent linear equations. Simulation and experiment are done to validate the dynamic model and the solution algorithm, and the results with high efficiency are accordant. The results show that according to the theory of Hamiltonian dynamics in phase-space, dynamics of parallel type six-axis accelerometer and the similar multi-body systems can be decoupled in the general work environment.