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A family of Runge-Kutta based explicit methods for rotational dynamics

Ghosh, S and Roy, D (2007) A family of Runge-Kutta based explicit methods for rotational dynamics. In: ASME 2007 International Mechanical Engineering Congress and Exposition (IMECE2007), November 11-15, 2007, Seattle, Washington.

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The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.

Item Type: Conference Paper
Publisher: ASME
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 03 Nov 2011 05:28
Last Modified: 03 Nov 2011 05:28
URI: http://eprints.iisc.ac.in/id/eprint/41727

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