A parallel Hamiltonian formulation for forward dynamics of closed-loop multibody systems

Krzysztof Chadaj , Paweł Malczyk , Janusz Frączek


This paper presents a novel recursive divide-and-conquer formulation for the simulation of complex constrained multibody system dynamics based on Hamilton’s canonical equations (HDCA). The systems under consideration are subjected to holonomic, independent constraints and may include serial chains, tree chains, or closed-loop topologies. Although Hamilton’s canonical equations exhibit many advantageous features compared to their acceleration based counterparts, it appears that there is a lack of dedicated parallel algorithms for multi-rigid-body system dynamics based on the Hamiltonian formulation. The developed HDCA formulation leads to a two-stage procedure. In the first phase, the approach utilizes the divide and conquer scheme, i.e., a hierarchic assembly–disassembly process to traverse the multibody system topology in a binary tree manner. The purpose of this step is to evaluate the joint velocities and constraint force impulses. The process exhibits linear O(n) (n – number of bodies) and logarithmic O(log2n) numerical cost, in serial and parallel implementations, respectively. The time derivatives of the total momenta are directly evaluated in the second parallelizable step of the algorithm. Sample closed-loop test cases indicate very small constraint violation errors at the position and velocity level as well as marginal energy drift without any additional form of constraint stabilization techniques involved in the solution process. The results are comparatively set against more standard acceleration based Featherstone’s DCA approach to indicate the performance of the HDCA algorithm.
Author Krzysztof Chadaj WMEiL
Krzysztof Chadaj,,
- Faculty of Power and Aeronautical Engineering
, Paweł Malczyk ITLMS
Paweł Malczyk,,
- The Institute of Aeronautics and Applied Mechanics
, Janusz Frączek ITLMS
Janusz Frączek,,
- The Institute of Aeronautics and Applied Mechanics
Journal seriesMultibody System Dynamics, ISSN 1384-5640 []
Issue year2017
Publication size in sheets1.3
Keywords in EnglishForward dynamics, Closed-loop systems, Hamilton’s canonical equations, Parallel algorithm, Divide and conquer, Joint coordinates
URL http://link.springer.com/article/10.1007%2Fs11044-016-9531-x
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 30.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.286 (2) - 2016=2.462 (5)
Citation count*5 (2018-07-16)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.