关键词: 哈密顿动力学, 解耦, 拉格朗日乘子, 四元数, 微分代数方程, 相空间

Abstract: 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 accelerometer are derived by transforming of Legende and using quaternions 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.

Key words: Decoupling, Differential algebraic equation, Hamiltonian dynamics, Lagrange multiplier, Phase-space, Quaternion