List of Works Cited
Bedford, A., & D. S. Drumheller, [1978]: A variational theory of immiscible mixtures. Arch. Rational Mech. Anal. 68, 37–51.
Bedford, A., & D. S. Drumheller, [1979]: A variational theory of porous media. Int. J. Solids Structures 15, 967–980.
Bedford, A., & D. S. Drumheller, [1983]: Theories of immiscible and structured mixtures. Int. J. Engng. Sci. 21, 863–960.
Bowen, R. M., [1976]: Theory of mixtures. In Continuum Physics, Vol. III, Mixtures and E. M. Field Theories, edited by A. C. Eringen. Academic Press.
Cowin, S. C., & M. A. Goodman, [1976]: A variational principle for granular materials. ZAMM 56, 281–286.
Craine, R. E., [1971]: Oscillations of a plate in a binary mixture of incompressible Newtonian fluids. Int. J. Engng. Sci. 9, 1177–1192.
Drew, D. A., [1976]: Two-phase flows: Constitutive equations for lift and Brownian motion and some basic flows. Arch. Rational Mech. Anal. 62, 149–163.
Drumheller, D. S., & A. Bedford, [1979a]: On the mechanics and thermodynamics of fluid mixtures. Arch. Rational Mech. Anal. 71, 345–355.
Drumheller, D. S., & A. Bedford, [1979b]: A theory of bubbly liquids. J. Acoust. Soc. Am. 66, 197–208.
Drumheller, D. S., & A. Bedford, [1980a]: A thermomechanical theory for reacting immiscible mixtures. Arch. Rational Mech. Anal. 73, 257–284.
Drumheller, D. S., & A. Bedford, [1980b]: A theory of liquids with vapour bubbles. J. Acoust. Soc. Am. 67, 186–200.
Drumheller, D. S., M. E. Kipp & A. Bedford, [1982]: Transient wave propagation in bubbly liquids. J. Fluid Mech. 119, 347–365.
Ericksen, J. L., [1961]: Conservation laws for liquid crystals. Transactions of the Society of Rheology 5, 23–34.
Ericksen, J. E., [1962]: Hydrostatic theory of liquid crystals. Arch. Rational Mech. Anal. 9, 379–394.
Finlayson, B. A., [1972]: The Method of Weighted Residuals and Variational Principles. Academic Press.
Graves, L. M., [1930a]: Discontinuous solutions in space problems in the calculus of variations. Am. J. Math. 52, 1–28.
Graves, L. M., [1930b]: Discontinuous solutions in the calculus of variations. Bull. Am. Math. Soc. 36, 831–846.
Graves, L. M., [1939]: The Weierstrass condition for multiple integral variational problems. Duke Math. J. 5, 656–660.
Gurtin, M. E., [1981]: An Introduction to Continuum Mechanics. Academic Press.
Hellinger, E., [1914]: Die allgemeinen Ansätze der Mechanik der Kontinua. In Encyklopädie der Mathematischen Wissenschaften, Band IV/4, edited by F. Klein & C. Müller. Teubner.
Herivel, J. W., [1955]: The derivation of the equations of motion of an ideal fluid by Hamilton's principle. Proc. Camb. Phil. Soc. 51, 344–349.
Hill, C. D., A. Bedford & D. S. Drumheller, [1980]: An application of mixture theory to particulate sedimentation. J. Appl. Mech. 102, 261–265.
Kirchhoff, G., [1876]: Vorlesungen über mathematische Physik: Mechanik. Leipzig.
Leech, C. M., [1977]: Hamilton's principle applied to fluid mechanics. Quart. J. Mech. Appl. Math. 30, 107–130.
Lichtenstein, L., [1929]: Grundlagen der Hydromechanik. Springer.
Mindlin, R. D., [1964]: Micro-structure in linear elasticity. Arch. Rational Mech. Anal. 16, 51–78.
Serrin, J., [1959]: Mathematical Principles of Classical Fluid Mechanics. In Handbuch der Physik, Band VIII/1, edited by S. Flügge & C. Truesdell. Springer-Verlag.
Taub, A. H., [1949]: On Hamilton's principle for perfect compressible fluids. Proceedings of Symposia in Applied Mathematics, Vol. 1, Non-linear Problems in Mechanics of Continua. American Mathematical Society.
Toupin, R. A., [1956]: The elastic dielectric, J. Rational Mech. Anal. 5, 849–915.
Truesdell, C., & W. Noll, [1965]: The Non-linear Field Theories of Mechanics. In Handbuch der Physik, Band III/3, edited by S. Flügge. Springer-Verlag.
Truesdell, C., & R. A. Toupin, [1960]: The Classical Field Theories. In Handbuch der Physik, Band III/1, edited by S. Flügge. Springer-Verlag.
Walter, A., [1868]: Anwendung der Methode Hamiltons auf die Grundgleichungen der mathematischen Theorie der Elastizität. Diss. Berlin.
Zemplén, G., [1905]: Besondere Ausführungen über unstetige Bewegungen in Flüssig-keiten. In Encyklopädie der Mathematischen Wissenschaften, Band IV/4, edited by F. Klein & C. Müller. Teubner.
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Communicated by H. F. Tiersten
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Batra, G., Bedford, A. & Drumheller, D.S. Applications of Hamilton's principle to continua with singular surfaces. Arch. Rational Mech. Anal. 93, 223–251 (1986). https://doi.org/10.1007/BF00281499
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DOI: https://doi.org/10.1007/BF00281499