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A Treatise on the Analytical Dynamics of Particles and Rigid Bodies

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
Author: E. T. Whittaker
Publisher: Cambridge University Press
Total Pages: 482
Release: 1988-12-15
Genre: Mathematics
ISBN: 9780521358835

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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.


A Treatise on Analytical Dynamics

A Treatise on Analytical Dynamics
Author: L. A. Pars
Publisher:
Total Pages: 641
Release: 1965
Genre: Science
ISBN: 9780918024077

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Analytical Mechanics

Analytical Mechanics
Author: John G. Papastavridis
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 1392
Release: 2014
Genre: Mathematics
ISBN: 9789814338714

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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.


Tensor Calculus and Analytical Dynamics

Tensor Calculus and Analytical Dynamics
Author: John G. Papastavridis
Publisher: Routledge
Total Pages: 435
Release: 2018-12-12
Genre: Mathematics
ISBN: 1351411624

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Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.


Analytical Mechanics

Analytical Mechanics
Author: A.I. Lurie
Publisher: Springer Science & Business Media
Total Pages: 859
Release: 2013-03-09
Genre: Technology & Engineering
ISBN: 3540456775

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This is a translation of A.I. Lurie’s classical Russian textbook on analytical mechanics. It offers a consummate exposition of the subject of analytical mechanics through a deep analysis of its most fundamental concepts. The book has served as a desk text for at least two generations of researchers working in those fields where the Soviet Union accomplished the greatest technological breakthrough of the 20th century - a race into space. Those and other related fields continue to be intensively explored since then, and the book clearly demonstrates how the fundamental concepts of mechanics work in the context of up-to-date engineering problems.


Analytical Mechanics

Analytical Mechanics
Author: J.L. Lagrange
Publisher: Springer Science & Business Media
Total Pages: 634
Release: 2013-04-17
Genre: Science
ISBN: 9401589038

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The Mécanique analytique presents a comprehensive account of Lagrangian mechanics. In this work, Lagrange used the Principle of Virtual Work in conjunction with the Lagrangian Multiplier to solve all problems of statics. For the treatment of dynamics, a third concept had to be added to the first two - d'Alembert's Principle - in order to develop the Lagrangian equations of motion. Hence, Lagrange was able to unify the entire science of mechanics using only three concepts and algebraic operations.


Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Total Pages: 530
Release: 2013-04-09
Genre: Mathematics
ISBN: 1475720637

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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.