Kinematics

Abstract

This chapter is dedicated to an extensive analysis of the kinematic aspects of a moving continuous system. After defining Eulerian and Lagrangian velocity and acceleration, the rate of deformation and the vorticity tensor are introduced to classify different flows: rigid, irrotational, and isochoric. Then, the transformation properties under a change of the frame of reference of these tensors are determined. A moving singular surface is defined together with its normal speed both in Eulerian and Lagrangian description of flow. Further, the kinematic compatibility conditions are determined for a singular moving surface. Some fundamental formulae to derive with respect to time some integrals evaluated on moving volumes or surfaces are proved. After a section of exercise, it is presented the program Velocity, written with Mathematica^®, to do the calculations showed in this chapter by a computer.