Orthogonal Complement Based DivideandConquer Algorithm for constrained multibody systems
 Rudranarayan M. Mukherjee,
 Kurt S. Anderson
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A new algorithm, Orthogonal Complement based DivideandConquer Algorithm (ODCA), is presented in this paper for calculating the forward dynamics of constrained multirigid bodies including topologies involving single or coupled closed kinematic loops. The algorithm is exact and noniterative. The constraints are imposed at the acceleration level by utilizing a kinematic relation between the joint motion subspace (or partial velocities) and its orthogonal complement. Sample test cases indicate excellent constraint satisfaction and robust handling of singular configurations. Since the present algorithm does not use either a reduction or augmentation approach in the traditional sense for imposing the constraints, it does not suffer from the associated problems for systems passing through singular configurations. The computational complexity of the algorithm is expected to be O(n+m) and O(log(n+m)) for serial and parallel implementation, respectively, where n is the number of generalized coordinates and m is the number of independent algebraic constraints.
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 Title
 Orthogonal Complement Based DivideandConquer Algorithm for constrained multibody systems
 Journal

Nonlinear Dynamics
Volume 48, Issue 12 , pp 199215
 Cover Date
 20070401
 DOI
 10.1007/s1107100690833
 Print ISSN
 0924090X
 Online ISSN
 1573269X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Closed kinematic loops
 Orthogonal complement
 Singular configurations
 Logarithmic computational complexity
 DivideandConquer
 Industry Sectors
 Authors

 Rudranarayan M. Mukherjee ^{(1)}
 Kurt S. Anderson ^{(1)}
 Author Affiliations

 1. Computational Dynamics Laboratory, Department of Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street., Troy, NY, 12180, USA