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Home > History and Archaeology > History > Dynamics; Or, a Treatise on Motion to Which Is Added a Short Treatise on Attractions
Dynamics; Or, a Treatise on Motion to Which Is Added a Short Treatise on Attractions

Dynamics; Or, a Treatise on Motion to Which Is Added a Short Treatise on Attractions


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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. 1844 Excerpt: ...that a couple applied to a body cannot move the centre of gravity. THIHD GENERAL PROBLEM. 200. A mixed system of bodies, either free or connected in any manner, and constrained by smooth fixed curve lines, surfaces, rigid rods, inextensible strings, 3/-c.; to determine equations for the motion of every such system free from tensions and reactions. We are enabled to do this by the principle of virtual velocities. For, when the effective forces have been reversed, the forces then acting on the system including tensions of rods and cords, and reactions of curve lines and surfaces, are such as would maintain equilibrium. Now the peculiarity of the principle of virtual velocities is that it furnishes an equation free from tensions, &c., and, consequently, if applied to a dynamical system, will furnish an equation containing only impressed and effective forces, without tensions and reactions. Let Sx, Syi, Sj, be any small arbitrary displacements which may be communicated to the particle mx, without deranging the system, i. e. without destroying contacts of particles with curve lines, &c.; Sx2, $y2, 5#2, 3#3, $y3, Szs... similar quantities for m2, m, ... Then by the principle of virtual velocities 2m (X-d- $x + m Y-d?y) Sy + m(Z-d- h = 0. 201. The great advantage of this equation consists in this, that it does not contain any terms depending on reactions and tensions. If the parts of the system be so connected as to render it impossible to displace one particle without disturbing all the others, it is obvious the virtual velocities for mx being assumed, those of all the other particles will be determinable by geometrical relations, and when so determined being written in the above equation, the coefficients of the arbitrary displacements being sep...


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Product Details
  • ISBN-13: 9781235292002
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 72
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1235292002
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 145 gr

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Dynamics; Or, a Treatise on Motion to Which Is Added a Short Treatise on Attractions
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