Lanterna Rally

Author: William N. Griffin

Publisher:

Published: 2015-07-22

Total Pages: 128

ISBN-13: 9781331979388

Excerpt from Solutions of the Examples Appended to a Treatise on the Motion of a Rigid Body Let Ob= a, Oa = b.(fig. l).If Pbe a point of the lamina whose co-ordinates are, y, the area of an element atP, whose sides are parallel to the axes of co-ordinates, is dx.dy, and this may also represent the mass of a corresponding element of the lamina if the mass of an unit of area of the lamina be unity; Now first the summation of the values of this function for elements which lie along the line Mq and form an elementary, strip of the body in that direction, is equivalent to integrating witli respect toy from y 0 toy Mq =a x)tan B.Hence for such, a strip 2(my F)becomes lja7(a-) ian=B = fia w- Zaa + w) tan B.Secondly, the required summation will be completed by adding the values of the function for such strips as those just considered, as they range from Oj to B, and this amounts to integrating the expression just obtained from. = pto a;= o;- .finally, 2(ma;y)=(J-f + i)anan Swhile M, the mass, has by virtue of the units adopted been represented by abi.-. S-imwy) Mab. h)Let, m, n be the cosines of the inclinations of this line to the co-ordinate axes; rthe distance of a point x, y, zin the line from its centre, and let the mass of an element at this point be represented by its length dr. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.