• Antonio Romano
  • Addolorata Marasco
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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.


Parametric Representation Rigid Motion Reference Configuration Material Derivative Particle Path 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonio Romano
    • 1
  • Addolorata Marasco
    • 1
  1. 1.Department of Mathematics and Applications “R. Caccioppoli”University of Naples Federico IINaplesItaly

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