Research on the Numerical Method of Nonlinear Rigidness/Flexibility Coupling Dynamics Equations of Flexible-Joint Flexible-Link Space Manipulator

The partial dynamics equations (PDE) of space manipulator with flexible-joint and flexible-link are modelled using the second Lagrange method. Then, the unstable quality of the conventional numerical integration methods under Lagrange system are appropriately proved through energy analysis; therefore, the precise integration method (PIM) under Hamilton system is adopted to solve the strictly stiff PDE owing to rigidness/flexibility coupling matter. The difficulty of transformation from Lagrange to Hamilton system is discussed when damping matrix is considered; and then, the state space vector method is introduced in order to obtain the Hamilton's equivalence form. The limitation of traditional PIM is pointed out and then a new dimension expanding PIM is presented, which converts the nonhomogeneous equations to homogeneous ones and avoids the inverse matrix calculation. Finally, the highly precise numerical results are acquired by computor simulation.