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Excerpt from Introductory Treatise on Rigid Dynamics It is hoped that the present work may meet the requirements of two classes of students. It is intended on the one hand to supply a clear account, complete as far as it goes, of the principles on which the calculation of the motion of a rigid body is conducted, for students who have not sufficient time to master the larger treatises already published on the subject. In addition, the writer's experience has shewn him that, in the case of students of a different class, the study of such a work as the present often forms a good preparation for an acquaintance with works which take a wider and deeper range. The chief difficulty experienced has been that of selection, from a large mass of propositions, of those which were proper to be included as of most importance. Stress has mainly been laid upon the clear enunciation of general principles, without a full perception of which there is sure to be confusion: while less importance has been attached to special artifices for the solution of particular problems. The author desires to express his thanks to several friends, and especially to his colleague Professor A. S. Herschel, for assistance in correcting proofs and for many valuable hints: and will be grateful to any of his readers who will inform him of errors, or suggest improvements. 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.
This is a comprehensive, state-of-the-art, treatise on the energetic mechanics of Lagrange and Hamilton, that is, classical analytical dynamics, and its principal applications to constrained systems (contact, rolling, and servoconstraints). It is a book on advanced dynamics from a unified viewpoint, namely, the kinetic principle of virtual work, or principle of Lagrange. As such, it continues, renovates, and expands the grand tradition laid by such mechanics masters as Appell, Maggi, Whittaker, Heun, Hamel, Chetaev, Synge, Pars, Luré, Gantmacher, Neimark, and Fufaev. Many completely solved examples complement the theory, along with many problems (all of the latter with their answers and many of them with hints). Although written at an advanced level, the topics covered in this 1400-page volume (the most extensive ever written on analytical mechanics) are eminently readable and inclusive. It is of interest to engineers, physicists, and mathematicians; advanced undergraduate and graduate students and teachers; researchers and professionals; all will find this encyclopedic work an extraordinary asset; for classroom use or self-study. In this edition, corrections (of the original edition, 2002) have been incorporated.
This classic book is a encylopaedic and comprehensive account of the classical theory of analytical dynamics. The treatment is rigorous yet readable, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration, and dissipative systems. Hamilton's principle is introduced and then applied to dynamical systems, including three-body systems and celestial mechanics. Very many examples and exercisies are supplied throughout.
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.
Beginning with the formula used to derive Euler dynamical equations, this book discusses Eulerian, Lagrangian and Hamiltonian approaches to generalized motion on rigid body in sequential chapters, emphasizing how one approach was extended and simplified by other one. The last chapter deals with canonical transformations from one phase space to other one, and invariance of certain properties including Poisson beackerts.