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On Geometry of Rotation Space-Introduction to Lie Group Modelling

The paper focus on mathematical modelling of rigid body rotation space from geometric point of view. The configuration of a rotating rigid body is given by a rotation matrix that belongs to Special Orthogonal Group SO(3). From the geometrical point of view, SO(3) can be considered as a differential manifold (space with different possibilities of parametarizations on which we can do calculus). Moreover, SO(3) has the properties of Lie-group, where the tangent space at the group identity I has an additional structure. This vector space is equipped with matrix commutator and constitutes Lie-algebra of SO(3), the set of skew-symmetric matrices denoted by so(3). Between the elements of Lie group and Lie algebra exists natural correspondence via exponential map that can be used for synthesis of the efficient numerical integration algorithms.

rigid body rotation field; SO(3) group; Lie group; kinematical constraints

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