Theoretical Mechanics An Introductory Treatise On the Principles of Dynamics Wi

Cover Theoretical Mechanics An Introductory Treatise On the Principles of Dynamics Wi
Theoretical Mechanics An Introductory Treatise On the Principles of Dynamics Wi
Love, A. E. H. (Augustus Edward Hough), 1863-1940
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199 This equation can be integrated when f{v) = kv^\ and we have 1 n/ gives t = — I - sec (f)dd(f) + const.
and thus the time and the position of the particle are determined in terms of a single parameter >.
It is not generally possible to integrate the equation for vertical rectilinear motion even for the case here described where /(v)=v". In the special case, however, where the resistance is proportional to the square of the velocity the velocity can be found in any position. We have, when th
...e particle is ascending, y = -g- Ky\ y being measured upwards. Now . Dy d, . . , y^^dy-^dy^^^^'^ hence ^(hf) + ''!/' = - 9- Multiplying by e^"'' and integrating, we have If^^y = -^ e-^y + const.

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