Opening page to Rudolf Clausius' 1875 Mathematical Introduction chapter. |
“Every force tends to give motion to the body on which it acts; but it may be prevented from doing so by other opposing forces, so that equilibrium results, and the body remains at rest. In this case the force performs no work. But as soon as the body moves under the influence of the force, work is performed.”
dW = S ds (1)where S is a component of the force (or FS in modern notation) action on a material point through a differential length of space ds. He then explains that, to facilitate further calculations, it is expedient to resolve both the direction of movement and the direction of the force into a Cartesian coordinate system, whereby the differential of work, in the two-dimensional case, becomes a function of force in the x- and y-directions:
dW = X dx + Y dy (3)
(4)
U = T + J