Abstract
Two alternative descriptions of motion are traditionally employed in Continuum Physics: the referential, in which fields are associated with material points and time, and the spatial in which the same fields are realized as functions of position and time. Hydrodynamicists commonly use the terms Lagrangean for referential and Eulerian for spatial but, as pointed out by Truesdell [3, §66A], the “Lagrangean” description was actually introduced by Euler while the “Eulerian” formulation was originally employed by Daniel Bernoulli and D’Alembert.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Diperna, R. J.: “Convergence of approximate solutions to conservation laws”, Arch. Rat. Mech. Anal. 82 (1983), pp. 27–70.
Gurtin, M. E., Williams, W. O., Ziemer, W. P.: “Geometric measure theory and the axioms of continuum thermodynamics”, Arch. Rat. Mech. Anal. 92 (1986), pp. 1–22.
Truesdell, C.A., Toupin, R.: “The Classical Field Theories”, Handbuch der Physik III/1, Springer-Verlag, Berlin 1960.
Wagner, D. H., “Equivalence of the Euler and the Lagrangian equations of gas dynamics for weak solutions”, J. Diff. Eqs. 68 (1987), pp.118–136.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Dafermos, C.M. (1993). Equivalence of Referential and Spatial Field Equations in Continuum Physics. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-322-87871-7_21
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-07643-6
Online ISBN: 978-3-322-87871-7
eBook Packages: Springer Book Archive