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XI.—The Modes of Vibration of a Stretched Membrane with a Particular Law of Density

Published online by Cambridge University Press:  15 September 2014

E. L. Ince
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Extract

In this paper it is proposed to study the problem of the vibrations of a uniformly-stretched membrane whose superficial density σ depends upon the distance r from a fixed point in the membrane in accordance with the law

in which C and a are constants. The constant a will be known as the critical radius and the circle r = a as the critical circle.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 45 , Issue 1 , 1926 , pp. 102 - 116
Copyright
Copyright © Royal Society of Edinburgh 1926

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References

page 103 note * Whittaker, and Watson, , Modern Analysis, chap. xviGoogle Scholar

page 105 note * Milne, A., Proc. Edin. Math. Soc, xxxiii (1915), p. 51.Google Scholar

page 105 note † Bôcher, , Leçons sur les méthodes de Sturm, chap. iii.Google Scholar, especially § 14.

page 107 note * Ann. Éc. Norm. (2), xiii (1883), p. 47.

page 107 note † Proc. Edin. Math. Soc., xxxiii (1914), p. 22.

page 107 note ‡ Proc. Lond. Math. Soc. (2), xxiii (1924), pp. 56–74.

page 108 note * Ince, , loc. cit., p. 65.Google Scholar

page 114 note * Whittaker and Watson, Modern Analysis, § 16·5.

page 115 note * Milne, , Proc. Edin. Math. Soc., xxxiii (1915), p. 59Google Scholar.