Multibody System Dynamics

, Volume 44, Issue 3, pp 251–275 | Cite as

Passivity-preserving splitting methods for rigid body systems

  • Elena Celledoni
  • Eirik Hoel Høiseth
  • Nataliya Ramzina


A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input–output passive. We propose passivity-preserving splitting methods for the numerical solution of a class of problems which includes this system as a special case. We prove the passivity-preservation property for the splitting methods, and we investigate stability and energy behaviour in numerical experiments. Implementation is discussed in detail for a special case where the splitting gives rise to the subsequent integration of two completely integrable flows. The equations for the attitude are reformulated on \(\mathit{SO}(3)\) using rotation matrices rather than local parameterisations with Euler angles.


Passivity Structure preservation Differential equations Time integration Multibody dynamics 



This work has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 691070, and from The Research Council of Norway. We are grateful to T.I. Fossen for useful discussions. We are also grateful to Sergio Blanes and Fernando Casas for useful discussions regarding splitting methods, and for providing highly accurate coefficients for the splitting methods of order 4 and 6 used in the numerical experiments. Part of this work was done while visiting Massey University, Palmerston North, New Zealand, and La Trobe University, Melbourne, Australia.


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

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNTNUTrondheimNorway

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