This paper reviews the Euler-Rodrigues formula in the axis-angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler-Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler-Rodrigues parameters and the Euler-Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler-Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics.


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    Title :

    Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections


    Contributors:
    Dai, Jian S (author)


    Publication date :

    2015




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    BKL:    52.20 Antriebstechnik, Getriebelehre / 50.32 Dynamik, Schwingungslehre / 50.25 Robotertechnik