In Stock with our New/Used Market Vendor. Allow up to 30 days for delivery. Tracking is not available for this item.
FREE Shipping is not available for this item.help
Southport, MERSEYSIDE, GBR
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 Excerpt: ... quantity of energy added to the system being zero. If a body be supposed at rest at any point of that portion of its path over wh1ch it has uniform motion, it will evidently remain there if subjected only to the system of forces which caused it to follow that path. In such a case the body is said to be in neutral or indifferent equilibrium. 156. To investigate the second case let us resume Eq. (132). The forces of gravitation, electricity, etc., or what are known generally as forces of nature, are taken to be constant or to vary as some function of the distance; and therefore Eq. (132) is applicable to a body subjected to their action, the normal reaction of the curve on which the body moves being considered as one of the extraneous forces. Assuming consecutive values of the kinetic energy of the body, we have, after developing the difference of the corresponding states of the function by Taylor's theorem, that is, the body will be in equilibrium when it reaches a position where it has a maximum or minimum kinetic energy. Let this condition be fulfilled, and we have If 1MV be a maximum the second member of this equation will have the negative sign, and whatever be the value of F, it must be greater than V; and if the body be slightly displaced from its position of equilibrium and then move from rest under the action of the given system of forces, the direction of the resultant must be such as to bring it back again. In this case the body would oscillate to and fro through its position of equilibrium, and could never depart far from it; the equilibrium of a body is therefore said to be stable when it occupies a position corresponding to a maximum value of its kinetic energy. If IfMV be a minimum the second member of Eq. (434) will be positive, and hence V...