Kinematics

Abstract

Kinematics is that division of Mechanics which describes the geometry of motion (deformation) of a body, regardless of the forces and stresses, the sources of that motion. Either the position or displacement vector, both the velocity and acceleration vector are key to analyzing the motion of a point. The fields of those vectors determine the kinematics of simple continua (point-continua). The deformation gradients, the spatial derivatives of the displacements, determine the local deformations and, hence, define the strains. Thus, the elongation of a fiber, the extension of a volume element, and the angular change of a configuration of two perpendicular fibers can be calculated. The kinematic model of a rigid (undeformable) body is characterized by a constant distance between any pair of points in motion. It is the principal reference system (eg for the deformations) and the velocity field is represented by means of the angular velocity vector. Polar cones of a spatial pendulum and polar curves (centrodes) associated with a rigid body in plane motion illustrate the velocity field of such an idealized model and introduce the notion of pure rolling contact.