Geometric algebra for multibody dynamics. Part II: Applications

In a companion paper, the fundamentals of vector space geometric algebra and plane-based geometric algebra were developed. Plane-based geometric algebra was found to be well suited for describing the kinematics of multibody dynamics: all required operations are performed using algebraic manipulations only and singularities are avoided altogether. The present paper presents applications of plane-based geometric algebra to problems of rigid and flexible multibody dynamics. The formulation of rigid bodies, flexible joints, geometrically exact beams, and lower-pair joints are developed.