Passivity-preserving splitting methods for rigid body systems

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 cla...

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Bibliographic Details
Published inarXiv.org
Main Authors Celledoni, Elena, Eirik Hoel Høiseth, Ramzina, Nataliya
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.04.2018
Subjects
Computer simulation
Differential equations
Euler angles
Mathematical models
Mathematics - Numerical Analysis
Numerical methods
Ordinary differential equations
Passivity
Rigid structures
Rigid-body dynamics
Splitting
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Summary: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 \(SO(3)\) using rotation matrices rather than local parametrizations with Euler angles.
ISSN:2331-8422
DOI:10.48550/arxiv.1408.2544