The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies Volume N . 1; Being Part I of a Treatise on the Whole Subject
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The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies Volume N . 1; Being Part I of a Treatise on the Whole Subject

The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies Volume N . 1; Being Part I of a Treatise on the Whole Subject


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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: ...To deduce the second set from the first, write p + iir for f. These results are giveu here for reference as they are useful in the higher problems of dynamics. 259. Small oscillations. It is clear that instead of referring the motion of the body to the principal axes at the fixed point, as Euler has done, we may use any axes fixed in the body. But these are in general so complicated as to be nearly useless. When, however, a body is making small oscillations about a fixed point, so that some three rectangular axes fixed in the body never deviate far from three axes fixed in space, it is often convenient to refer the motion to these even though they are not principal axes. In this case w1, w2, w3 are all small quantities, and we may neglect their products and squares. The general equation of Art. 252 reduces in this case to Ci3-Dw2-Ed1 = N, where the coefficients have the usual meanings given to them in Chap. i. We have thus three linear equations which may be written thus: Ai-FC2-Ew3=L, -Fd1 +Bu2-Du3 = M, - ti, -Da2 + Cw3=N. 260. The centrifugal forces. It appears from Euler's Equations that the whole changes of u, big, u3 are not due merely to the direct action of the forces, but are in part due to the centrifugal forces of the particles tending to carry them away from the axis about which they are revolving. For consider the equation N A-B Of the increase du3 in the time dt, the part--dt is due to the direct action of C the forces whose moment is Ar, and the part-J uwjlt is due to the centrifugal forces. This may be proved as follows. If a body be rotating about an axis 01 with an angular velocity u, then the moment of the centrifugal forces of the wliole body about the axis Oz is (A-B) UjW2. Let P be the position of any particle nt, and let x, y, z be ...


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Product Details
  • ISBN-13: 9781153822718
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 188
  • Spine Width: 10 mm
  • Width: 189 mm
  • ISBN-10: 1153822717
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 345 gr

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The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies Volume N . 1; Being Part I of a Treatise on the Whole Subject
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