A Treatise on the Mathematical Theory of the Motion of Fluids

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Overview

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1879 Excerpt: ... w, q, r are small quantities whose squares and products we may neglect. The first of (20) then gives 3-= 0, or u = const., and the remaining equations become BTt= (AuU G§= A-B)u + Uv. Eliminating r, we find BQ =-(Au + tt(A-B)u + &v (48). Exactly the same equation is satisfied by w. It is therefore ...
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A treatise on the mathematical theory of the motion of fluids

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Overview

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1879 Excerpt: ... w, q, r are small quantities whose squares and products we may neglect. The first of (20) then gives 3-= 0, or u = const., and the remaining equations become BTt= (AuU G§= A-B)u + Uv. Eliminating r, we find BQ =-(Au + tt(A-B)u + &v (48). Exactly the same equation is satisfied by w. It is therefore necessary and sufficient for. stability that the coefficient of v on the Phil. Mag. Nov. 1871. right-hand side of (48) should he negative; and the time of a small oscillation, in the case of disturbed stable motion, is BQ 123. The general equations of motion of the ring are also satisfied by 77, f, X, fi = 0, and v constant. We have then M =--, r = const. A The motion of the ring is then one of uniform rotation about an axis in the plane yz parallel to that of y, and at a distance from it. Case of two or more moving solids. 124. The foregoing methods fail when we have two or more moving solids, or when the fluid does not extend in all directions to infinity, being bounded externally by fixed rigid walls. In such cases we may suppose the position at the time t of each moving solid to be defined by means of six 'co-ordinates,' in the manner explained in treatises on Kinematics. It is easy to see that j must be a linear function of the rates of variation of these coordinates (in other words, of the 'generalized velocity-components' of the system), and thence that the kinetic energy of the system is, as in Art. 110, a homogeneous quadratic function of these generalized velocities, with however the important change that the coefficients in this function are not constants, but themselves functions of the co-ordinates of the system. The equations of motion are then most conveniently formed by Lagrange's method, the applicability of which to systems of the pecul...
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Product Details

  • ISBN-13: 9781151452733
  • Publisher: Rarebooksclub.com
  • Publication date: 5/28/2012
  • Pages: 74
  • Product dimensions: 7.44 (w) x 9.69 (h) x 0.15 (d)

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