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A Treatise on Infinitesimal Calculus, Vol. 4: Containing Differential and Calculus Volume Calculus (Classic Reprint) - Softcover
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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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A Treatise on Infinitesimal Calculus, Vol 4 Containing Differential and Calculus Volume Calculus Classic Reprint
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A Treatise on Infinitesimal Calculus, Vol 4 Containing Differential and Calculus Volume Calculus Classic Reprint
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A Treatise on Infinitesimal Calculus, Vol 4 Containing Differential and Calculus Volume Calculus Classic Reprint
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A Treatise on Infinitesimal Calculus, Vol 4 Containing Differential and Calculus Volume Calculus Classic Reprint
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A Treatise on Infinitesimal Calculus, Vol. 4 (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book explores the dynamics of material systems, analyzing the motion of a system as a whole. The author presents the subject using a geometric approach to complicated mechanical laws, introducing geometrical theorems, and applying these to the study of rigid bodies in motion. The book makes extensive use of the symbolism of analytical geometry and symmetrical manipulation and outlines principles which they involve, such as the transformation of the equations of rotation into angular velocities, the geometry of masses, and the theory of principal axes. The author demonstrates theorems important in reference to these equations, discovered by Poisson, Jacobi, Prof. Donkin himself, M. Bour, M. Liouville, and provides a conclusive chapter on theoretical dynamics which discusses the number and order of the differential equations of motion in the most general problem, the possibility of the solution of some or all of them, and the forms of the resulting integrals. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781333155148_0
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