Acta Mechanica

, Volume 73, Issue 1–4, pp 239–244 | Cite as

A note on the equivalence of shock manifold equations

  • R. Roy
  • R. Ravindran


The shock manifold equation is a first order nonlinear partial differential equation, which describes the kinematics of a shockfront in an ideal gas with constant specific heats. However, it was found that there was more than one of these shock manifold equations, and the shock surface could be embedded in a one parameter family of surfaces, obtained as a solution of any of these shock manifold equations. Associated with each shock manifold equation is a set of characteristic curves called ‘shock rays’. This paper investigates the nature of various associated shock ray equations.


Differential Equation Manifold Dynamical System Partial Differential Equation Fluid Dynamics 
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    Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. 2, New York: Interscience 1962.Google Scholar
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    Maslov, V. P.: Propagation of shock waves in an isentropic nonviscous gas. J. Soviet Math.13, 119–163 (1980).Google Scholar
  3. [3]
    Prasad, P.: Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas. Acta Mech.45, 163–176 (1982).Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • R. Roy
    • 1
  • R. Ravindran
    • 1
  1. 1.Department of Applied MathematicsIndia Institute of ScienceBangaloreIndia

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