Homogeneous Rigid Body Mechanics with Elastic Coupling
Geometric algebra is used in an essential way to provide a coordinate-free approach to Euclidean geometry and rigid body mechanics that fully integrates rotational and translational dynamics. Euclidean points are given a homogeneous representation that avoids designating one of them as an origin of coordinates and enables direct computation of geometric relations. Finite displacements of rigid bodies are associated naturally with screw displacements generated by bivectors and represented by twistors that combine multiplicatively. Classical screw theory is incorporated in an invariant formulation that is less ambiguous, easier to interpret geometrically, and manifestly more efficient in symbolic computation. The potential energy of an arbitrary elastic coupling is given an invariant form that promises significant simplifications in practical applications.
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