By William Frederick Durand
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer booklet information 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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Extra resources for Aerodynamic Theory: A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
A vector expressed as x + i y is therefore to be understood as directing that a length x be laid off along the direction of X followed by a length y laid off at + 90° to the same axis. It should be noted that here, y does not, in itself, imply a length laid off in the direction of y, but simply a length, while the i operator tells us that this length is to be laid off at + 90° to the axis of scalars, or here in the direction of + Y. : such axis. X The representation of the vector is comFig. 12.
The present development extends this same relation to lines having any direction in the plane. If therefore in Fig. 10, AB means a vector taken in the sense A to B, then - AB means the same vector reversed or taken in the sense B to A. Hence with this understanding regarding the significance of the order of the letter designating a vector, we may write - AB = BA or- BA = AB. Attention may be here drawn to the distinction between the designation of a vector in the form + z= x i y and x, y Z= where the latter gives merely the x and y components of the scalar length, but without algebraic relation between them.
Otherwise we may reach the same result by taking the X and Y components of the various vectors: Thus denoting any vector in general iy1 ~ 1 = x1 by z we may write: z2 = x2 + iy2 ~3 = Xa + iya ~4= x4+ iy4 i I: y. Then X z = I: x But in the numerical sense the value of I: x will be the same whatever the order in which the individual values are taken, and the same for I: y. Hence no matter what the order of the vectors, the values of I: x and I: y will be the same. But these are the X and Y components of the final vector sum X z and hence the resultant vector Xz = 1: x + i I: y will be the same no matter in what order the individual vectors may be taken.