Abstract
This paper is concerned with the analytical solution of two related mathematical problems which arise in mechanics and optics. Problem I consists of determining analytically for a given ellipsoid the directions of the principal axes of any plane elliptical section. It arises when dealing with electromagnetic plane waves in homogeneous, non-conducting, non-opti-cally active, magnetically isotropic media, characterized by an electric permittivity tensor k (see, for instance [1] or [2]). Indeed, the directions of vibration of the electric displacement D of the two homogeneous waves that may propagate in any direction n lie along the principal axes of the elliptical section by the plane n · x = 0 of the “index ellipsoid” x · k -1 x = 1.
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Dedicated to Paul M. Naghdi on the occasion of his 70th birthday
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© 1995 Birkhäuser Verlag Basel/Switzerland
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Boulanger, P., Hayes, M. (1995). The common conjugate directions of plane sections of two concentric ellipsoids. In: Casey, J., Crochet, M.J. (eds) Theoretical, Experimental, and Numerical Contributions to the Mechanics of Fluids and Solids. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9229-2_19
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DOI: https://doi.org/10.1007/978-3-0348-9229-2_19
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