Introduction Volume 21, No. 1
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Introduction Volume 21, No. 1

Introduction Volume 21, No. 1


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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. 1876 Excerpt: ...as h is or is not equal to j. Then, by putting do, we shall have--1--O' dL dt--ii2 (24) _ D' fc----"s- These 3ra equations, combined with the Sn equations (23), will give, by simple integration by quadratures, the perturbation of the 6n constants, which, being substituted in the original equations (12), will give values of the variables which satisfy the original differential equations to terms one order higher than they were satisfied by (12) originally. It will be observed that if our functions of the time and 6't arbitrary constants, which we have represented by %, ri, and -, possessed the property that a function A) f 7j and could be found such that for all values of % 6%?o0 d% _ do. d% _?no 5. Fundamental Relation between the Coefficients of the time, bu b2, etc., considered as Functions of cx, c2, etc. In the preceding section we have found ourselves able to express the first approximate values of the variables in terms of 3- pairs of arbitrary constants Cj l2 in which the two members of each pair are conjugate to each other; or possess the property that the expressions (14) all vanish except when ak and at represent the two members of a conjugate pair, in which case we have et) = + 1. (25) The distinguishing characteristic of the integrals we have been investigating is that they do not contain the time, except as multiplied by the 3- factors b, which are functions of the Sn constants c. This characteristic will enable us to deduce a fundamental relation between the differential coefficients of b with respect to c. In the first place, we remark that each c has a & to which it stands in a peculiar relation, in that the latter, multiplied by the time, is added to the I, which is conjugate to c to f...


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Product Details
  • ISBN-13: 9781235936968
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 112
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 1235936961
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 213 gr


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