Momentum Cloud Method for Dynamic Simulation of Rigid Body Systems
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A new formulation of multibody dynamics, the momentum cloud method (MCM), is presented. The method is based on applying the conservation of momentum directly to a complete system, and makes use of prescribed motions between each contiguous body. The absolute translation and rotation of a prescribed base body within the system are chosen to be reference point coordinates. The relative rotations between contiguous bodies along the kinematic chain within the system are chosen to be relative coordinates, the effect of which are captured as a series of cascading transformation matrices. The final result is that the motion of an N-body system can be represented conveniently using only six equations of motion (EOM). Numerical integration of these EOM is facilitated by representing the mass matrix of the entire system as two 333 matrices. The solutions to three coupled rotational EOM based on conservation of angular momentum of the system are Euler angles describing the rotation of the base body. The solutions to three coupled translational EOM based on conservation of linear momentum of the system are the translation of the system measured at its center of mass (CM), which are then transferred into translation of base body. Additionally, the inverse dynamic analysis can be used to obtain internal forcing between any two contiguous bodies. The new method is derived for a generalized serial N-body system connected by revolute joints with prescribed relative rotation, and then expanded to more complicated forms and joints.Asimulation example is presented for a six-body floating wind turbine system.DOI:10.1061/(ASCE)EM.1943-7889.0000634. © 2014 American Society of Civil Engineers.
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