Multibody System Dynamics

, Volume 45, Issue 3, pp 315–359 | Cite as

A path following method for identifying static equilibrium in multi-body-dynamic systems

  • Geoffrey K. RoseEmail author
  • Brett A. Newman
  • Duc T. Nguyen


Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static solvers. Analysts are often faced with uncertainty in regards to the values of candidate equilibrium states or whether a state of minimum potential energy was found. In the event of static solver failure or uncertainty with regards to a candidate solution, equilibrium could be obtained through a dynamic simulation which may require the addition of artificial damping. However, this method can have significant computational expense as compared to static solution procedures. Using MBD systems representing a pendulum, two variations of a spring supported arch, and a seven-body mechanism, arc-length solvers were found suitable for identifying equilibrium states through a robust production of static solution curves thereby avoiding dynamic simulation. Using these examples, a procedure for finding the correct equilibrium state for general systems is proposed.


Path following Arc-length method Nonlinear equations Multi-body-dynamics 



This work was funded by the Advanced Degree Program at NASA Langley Research Center.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Structural Dynamics BranchNASA Langley Research CenterHamptonUSA
  2. 2.Department of Mechanical and Aerospace EngineeringOld Dominion UniversityNorfolkUSA
  3. 3.Department of Civil and Environmental EngineeringOld Dominion UniversityNorfolkUSA

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