By William Frederick Durand
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer publication data mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Additional resources for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
1) by cos n 0 and integrate as before between limits of - n and n. 4) If, therefore, the function is known between limits of - n and + n for () (corresponding to - x and + x as in Fig. 5) the various coefficients may be found by any suitable process of integration. 2. Fourier Series Continued. 1) is applicable only when the values at C and D Fig. 5 are the same. This is obvious from the form of the equation. Let us now consider two special cases as represented in Fig. 6. First take the function represented by C ED, symmetrical about y.
Operating on a vector z 1 by a vector Z 2 as a divisor will be to divide the scalar value r 1 by r 2 and to swing the vector through an angle + + + + + + + + + -02. Multiplication by a vector therefore revolves the vector operated on through a angle and division by a vector revolves it through a - angle. This is all consistent with the mutually reciprocal relations of multiplication and division. As in algebra, multiplication and division by the same factor will cancel; so here with vectors, multiplication and division by the same vector leave the original vector unchanged.
To examine the case for vector quantities we first ask whether, in AB BC = BC AB the vector sense The meaning of this is: Starting from an initial point A and executing first a vector with the specifications of AB and then in sequence a vector with the specifications of BC, thus arriving at 0, will the result be the same if instead we should take the c vectors in the inverse order 1 In Fig. 14 let AB and BC denote the vectors in question. Complete the parallelogram A BCD. Then from the addition theorem: 0 AC=AB+ BC Fig.