Baecklund transformations, the inverse scattering method, by Robert M. Miura PDF

By Robert M. Miura

ISBN-10: 3540076875

ISBN-13: 9783540076872

Court cases of the NSF examine Workshop on touch changes, Held in Nashville, Tennessee, 1974

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Additional info for Baecklund transformations, the inverse scattering method, solitons, and their applications

Example text

And the supports are not on the Statique Graphique, t. slightly compressible has been treated by Prof Pearson in the Messenger of Mathematics, xix. 1890. Basis of Graphic Method \ We have seen how a knowledge of the bending moment at every point of a beam resting on supports leads to a determination of the form assumed by the beam and the pressures on the supports, 224. 1 For references see Introduction p. 12. BENDING OF RODS IN ONE PLANE. 42 [224? and further how the bending moment at any point can be determined from those at the extremities of the span containing it, and we have given the equations by which the bending moments at We shall now shew how the consecutive supports are connected.

1773. 4 — 193. 22 HISTORICAL INTRODUCTION. concluded that for shorter lengths it will be simply compressed while for greater lengths it will be bent. The problem of Euler was the only problem in Elastic Stability attempted many years. It found its way into practical treatises on the Resistance of Materials as Heim's Gleichgewicht und for * ', elastischer fester Bewegung gespannter Korper^ and Bresse's Cours de Mecanique Appliquee ^. Meanwhile Lamarle^ pointed out that, unless the length be very great compared with the diameter, a load great enough to produce buckling will be more than great enough to produce set.

Cussion of the circular He followed Kirchhoff in the dis- plate, and gave the solutions Note du § 73. of the 1 In the 'Annotated Clebsch ^ Liouville's Journal, xvi. 1871. 2 Proc. Lond. Math. Sac. xxi. 1890. ^ j^i^^, y, ' Ibid. « ', 1379. Theory of Sound, vol. i. 2—2 ch. x. HISTORICAL INTRODUCTION. 20 frequency-equation for the lowest tones and the character of the nodal lines. He remarked that if there are any materials which when they are slightly extended longitudinally, rectangular plates of such materials can vibrate like bars without being supported at the edges.

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Baecklund transformations, the inverse scattering method, solitons, and their applications by Robert M. Miura

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