On the Adjoint Formulation of Design Sensitivityanalysis of Multibody Dynamics: the Piecewise Adjoint Method for Design Sensitivityanalysis (Dsa) of ... Dynamicswith Euler Parameters for Orientation

A modified Adjoint method is presented, in which computation can be distributed to 2d+2 processors,where d is the number of degrees of freedom of themultibody system, and the Adjoint backward initialvalue problem (IVP) is replaced by a boundary valueproblem (BVP), which is solved through a backwardmultiple shooting algorithm. In the equivalent BVPformulation, each time-step is solved in the backwarddirection, but time-steps advance in the forwarddirection. As a result, the memory load for storinggeneralized coordinates during integration of the DAEof motion, is minimized. The specific objectives are (...) to develop a newmethod, called the Piecewise Adjoint method, that (1)requires the integration of a number of DAE that doesnot depend on the number of design parameters; (2)has a parallel computational structure; (3)progresses forward in time; and (4) minimizes thememory load required by the backward integration ofthe Adjoint DAE.