This work applies geometric algebra to modeling of elastically coupled rigid bodies, with application to modeling and computer simulation of spatial, flexural mechanisms. Euclidean space E(3) is modeled homogeneously as a three-dimensional horosphere of null vectors in the Minkowski space R(4,1). Associated with the Minkowski space is a geometric algebra.

Finite, elastic displacements of rigid bodies can be associated naturally with screw displacements. Alternatively, elastic displacements can be associated with spinors, which are exponentials of half-twists. Both twists and spinors can be represented using the Minkowski geometric algebra.

The potential energy of an arbitrary elastic coupling in internal equilibrium can be represented as (1) a finite-order polynomial of twist coefficients, or (2) a finite-order polynomial of spinor coefficients. Both possibilities are investigated in the paper. Such polynomials have been investigated previously using dual-number, matrix methods. Use of geometric algebra results in less ambiguous expressions that are easier to interpret geometrically.

The intended application of the methods is dynamic simulation of spatial, flexural mechanisms. Some discussion of this problem is given, although readers are referred to other papers for details.

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