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Most current linear-time forward dynamics algorithms support only simple types of joints due to difficulties in computing derivatives of joint transformations up to order two. We apply the D* symbolic differentiation algorithm to a recursive formulation of forward dynamics to get a highly efficient linear-time forward dynamics algorithm supporting multibody systems with general scleronomic joints. With this new algorithm we can easily build a tree-topology multibody system with complex joint models and perform forward dynamics efficiently. The source code for the algorithm is freely available for non-commercial use.

Linear-time dynamics for multibody systems with general joint models