Graphical Methods a Course of Lectures Delivered in Columbia University New Yo
Graphical Methods a Course of Lectures Delivered in Columbia University New Yo
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Over the curve D = in the uv plane, corresponds to a line running from one of the sheets onto the other. It need not change its direction abruptly when it reaches the rim and passes onto the other sheet. For it may touch the rim in the direction of its tangent. This is actually the rule and the abrupt change of direction is the exception. Any line LAL (Fig. 55) in the uv plane, whose tangent as it crosses the curve D = at A does not coincide with the common tangent of the curves x = const, and ...y = const, will correspond to a line in the xy plane, that does not change its direction abruptly when it touches the rim. This is best understood analytically. Let us consider corre- sponding directions at the points A in the uv plane and in the xy plane. We have seen above that corresponding directions (Fig. 56) are connected by the equations 78 GRAPHICAL METHODS. Dy/dr- dx/dr FIG. 56. u cos a + v sin a, ds dy - = -7- = ^u cos a + ^ c sm a. At the point A we have Assuming that the gradients at A do not vanish, so that we can write MoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Over the curve D = in the uv plane, corresponds to a line running from one of the sheets onto the other. It need not change its direction abruptly when it reaches the rim and passes onto the other sheet. For it may touch the rim in the direction of its tangent. This is actually the rule and the abrupt change of direction is the exception. Any line LAL (Fig. 55) in the uv plane, whose tangent as it crosses the curve D = at A does not coincide with the common tangent of the curves x = const, and ...y = const, will correspond to a line in the xy plane, that does not change its direction abruptly when it touches the rim. This is best understood analytically. Let us consider corre- sponding directions at the points A in the uv plane and in the xy plane. We have seen above that corresponding directions (Fig. 56) are connected by the equations 78 GRAPHICAL METHODS. Dy/dr- dx/dr FIG. 56. u cos a +
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