Multibody System Dynamics

, Volume 18, Issue 2, pp 145–168

Efficient methodology for multibody simulations with discontinuous changes in system definition


DOI: 10.1007/s11044-007-9075-1

Cite this article as:
Mukherjee, R.M. & Anderson, K.S. Multibody Syst Dyn (2007) 18: 145. doi:10.1007/s11044-007-9075-1


A new method is presented for accurately and efficiently simulating multi-scale multibody systems with discontinuous changes in system definitions as encountered in adaptive switching between models with different resolutions as well as models with different system topologies. An example of model resolution change is a transition of a system from a discrete particle model to a reduced order articulated multi-rigid body model. The discontinuous changes in system definition may be viewed as an instantaneous change (release or impulsive application of) the system constraints. The method uses a spatial impulse–momentum formulation in a divide and conquer scheme. The approach utilizes a hierarchic assembly–disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The method is applicable for systems in serial chain as well as kinematical loop topologies. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The equations of motion for the system are produced in a hierarchic sub-structured form. This has the advantage that changes in sub-structure definitions/models results in a change to the system equations only within the associated sub-structure. This allows for significant changes in model types and definitions without having to reformulate the equations for the whole system.


Impulse momentum formulation Divide and conquer scheme Logarithmic complexity Course-graining of models Discontinuous system definitions 

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mechanical, Aeronautical, and Nuclear EngineeringRensselaer Polytechnic InstituteTroyUSA