Advertisement

Kinematics

  • Antonio Romano
  • Addolorata Marasco
Chapter
  • 2.4k Downloads
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

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.

Keywords

Parametric Representation Rigid Motion Reference Configuration Material Derivative Particle Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [9]
    F. Dell’Isola, A. Romano, On a general balance law for continua with an interface. Ricerche Mat. 2, XXXV (1986)Google Scholar
  2. [16]
    M. Gurtin, On the two-phase Stefan problem with interfacial entropy and energy. Arch. Rat. Mech. Anal. 96, 199–241 (1986)MathSciNetzbMATHGoogle Scholar
  3. [34]
    A. Marasco, A. Romano, Balance laws for charged continuous systems with an interface. Math. Models Methods Appl. Sci. (M3AS) 12(1), 77–88 (2002)Google Scholar
  4. [37]
    G.P. Moeckel, Thermodynamics of an interface. Arch. Rat. Mech. Anal. 57, 255–280 (1974)MathSciNetCrossRefGoogle Scholar

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

Personalised recommendations