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    The Computations of Large Rotation Through an Index Two Nilpotent Equation

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 157-176, 2006, DOI:10.3970/cmes.2006.016.157

    Abstract To characterize largely deformed spin-free reference configuration of materials, we have to construct an orthogonal transformation tensor Q relative to the fixed frame, such that the tensorial equation Q˙ = WQ holds for a given spin history W. This paper addresses some interesting issues about this equation. The Euler's angles representation, and the (modified) Rodrigues parameters representation of the rotation group SO(3) unavoidably suffer certain singularity, and at the same time the governing equations are nonlinear three-dimensional ODEs. A decomposition Q = FQ1 is first derived here, which is amenable to a simpler treatment of Q1 than Q, and… More >

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