A Treatise on Infinitesimal Calculus, Vol 4 Containing Differential and Calculus Volume Calculus Classic Reprint

Excerpt from A Treatise on Infinitesimal Calculus, Vol. 4: Containing Differential and Calculus Volume Calculus

Although I have entitled the present Volume, Dynamics of Material Systems; yet the investiga tions contained in it are far from comprising all which a complete treatise on that subject requires. They are indeed almost wholly confined to those par ticular systems in which the internal forces, brought into action, either effectively or potentially, by means of the external forces, enter in equal and opposite pairs; so that they disappear in the equations of motion formed on d'alembert's principle. I say almost wholly, because, in the last Chapter but one of the Volume, the motion of the particles of an elastic body is to a certain extent discussed: and herein the elastic forces, which are internal forces, do not disappear, but enter as effective forces, the action of which is determined by Hooke's law, or by an equivalent assumption of a property of such matter. In all other cases, in a rigid body, in a rigid system which is maintained in a state of rela tive rest by rigid rods and similar modes of con straint, in systems wherein every mutual action of attraction or repulsion is accompanied by an equal and opposite reaction, the internal forces disappear from the equations of motion.

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