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On whether elastic wave surfaces possess cuspidal edges

Published online by Cambridge University Press:  24 October 2008

M. J. P. Musgrave
M. J. P. Musgrave
Affiliation:
National Physical LaboratoryTeddington
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Abstract

Consideration of the direction of the normal at any point on a continuous sheet of a surface yields a sufficient condition for the existence of parabolic points on that sheet. This condition has been used to derive some simple inequalities between elastic constants, whose fulfilment determines the existence of parabolic points upon the inverse surfaces of media of orthorhombic, tetragonal, cubic or hexagonal symmetry; in virtue of the polar reciprocal relation between inverse and wave surfaces, the existence of cusp points on the latter is thereby simultaneously established. It is also pointed out that conditions for external conical refraction may prevail in hexagonal media.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 897 - 906
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

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