ABSTRACT
Geometric complexity is the principal hindrance to in-depth biomechanical analyses. This chapter reviews elementary methods for organizing and studying complex geometrical systems. These methods include vector, dyadic, and matrix algebra, index notation, and determinants. Vectors are usually first encountered in elementary physics in the modeling of forces. The chapter utilizes vectors to represent not only forces but also kinematic quantities such as position, velocity, and acceleration. Two special and frequently occurring vectors form the basis for vector algebra and analysis. These are zero vectors and unit vectors. Dyadics are useful in continuum mechanics for the representation the of stress and strain. In dynamics, dyadics represent inertia properties of bodies. Two prominent scalar measures of square matrices are the trace and the determinant. The trace is the sum of the elements on the diagonal. For square matrices, the determinant is a number used as a measure of the matrix.
