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Home > History and Archaeology > History > The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies; Being Part I. of a Treatise on the Whole Subject; With Numerous Examples
The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies; Being Part I. of a Treatise on the Whole Subject; With Numerous Examples

The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies; Being Part I. of a Treatise on the Whole Subject; With Numerous Examples


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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. 1905 Excerpt: ...consider the equation N A-B Of the increase du3 in the time dt, the part--dt is due to the direct action of w, dt is due to the centrifugal C the forces whose moment is N, and the part forces. This may be proved as follows. If a body be rotating about an axis OI with an angular velocity u, then the moment of the centrifugal force- of the whole body about the axis Oz it (A-B) W; w2. Let P be the position of any particle m, and let.;', //, z be its coordinates. Then x = OR, y = RQ, z = QP. Let PS be a perpendicular on OI, let OS = u, and PS=r. Then the centrifugal force of the particle m is u2TM tending from 01. The force w2rni is evidently equivalent to the four forces u-xm, wym, u-zm, and-u-um acting at P parallel to x, y, z, and u respectively. The moment of uPxm round Oz is-u-xym, while that of u'ym is the same with an opposite sign. The moment of ufzm round Oz is zero. These three therefore produce no effect. The force-uaum parallel to 01 is equivalent to the three, -tiu um, -i-', '..//;-, -ua3um, acting at P parallel to the axes, and their moment round Oz is evidently wum (uy-u.2x). Now the direction-cosines of 01 being wju, u.2/u, w3/6j, we get by projecting the broken line.r, y, z on 01, therefore substituting for u, the moment of centrifugal forces about Oz is = (al-xy + wla.2y'-+ w1ta3yz Writing 2 before each term, and supposing the axes of x, y, z to be principal axes, then the moment of the centrifugal forces about the principal axis Oz = fc! u3 2w (y'-x) = Mj w, (A-B). Let the moments of the centrifugal forces about the principal axes of the body be represented by L', M', N', so that and let H be their resultant couple. This couple is usually called the centrifugal couple. Since L'al + M'u, + N'u3--0, it follows that the axis of the centrif...


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Product Details
  • ISBN-13: 9781231914588
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 186
  • Spine Width: 10 mm
  • Width: 189 mm
  • ISBN-10: 1231914580
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 340 gr

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The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies; Being Part I. of a Treatise on the Whole Subject; With Numerous Examples
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