Theoretical Mechanics With An Introduction To The Calculus
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| Author | : Mark Levi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 322 |
| Release | : 2014-03-07 |
| Genre | : Mathematics |
| ISBN | : 0821891383 |
This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
| Author | : Joseph Sweetman Ames |
| Publisher | : |
| Total Pages | : 480 |
| Release | : 1929 |
| Genre | : Mathematical physics |
| ISBN | : |
| Author | : Julius Weisbach |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 1102 |
| Release | : 2024-01-31 |
| Genre | : Fiction |
| ISBN | : 3382832690 |
Reprint of the original, first published in 1875. The publishing house Anatiposi publishes historical books as reprints. Due to their age, these books may have missing pages or inferior quality. Our aim is to preserve these books and make them available to the public so that they do not get lost.
| Author | : V.I. Arnol'd |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 530 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 1475720637 |
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.
| Author | : Sir James H. Jeans |
| Publisher | : Courier Corporation |
| Total Pages | : 381 |
| Release | : 2013-05-23 |
| Genre | : Science |
| ISBN | : 0486174697 |
In addition to being among the twentieth century’s major scientific figures, Sir James Jeans (1877–1946) was also one of the greatest modern science expositors. His classic introduction to mechanics endures as a clear and concise presentation of first principles. Although brief, it encompasses a remarkably wide selection of topics. Its subjects include rest and motion, force and the laws of motion, forces acting on a single particle, statics of systems of particles, statics of rigid bodies, center of gravity, work, motion of a particle under constant forces, motion of systems of particles, motion of a particle under a variable force, motion of rigid bodies, and generalized coordinates. Within each chapter, the author carefully explains the most elementary concepts (such as velocity, acceleration, Newton’s laws, friction, moments, and kinetic energy), and he illustrates them with examples. Ideal for beginning physics students or for more advanced readers in need of refreshment, the text emphasizes the fundamental physical principles rather than mathematics or applications. So clearly written that it can be read and understood outside the classroom, it features hundreds of fully worked illustrative examples and test exercises.
| Author | : Julius Weisbach |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 1114 |
| Release | : 2024-05-08 |
| Genre | : Fiction |
| ISBN | : 3385257174 |
Reprint of the original, first published in 1875.
| Author | : John G. Papastavridis |
| Publisher | : Routledge |
| Total Pages | : 435 |
| Release | : 2018-12-12 |
| Genre | : Mathematics |
| ISBN | : 1351411624 |
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.
| Author | : Hans Sagan |
| Publisher | : Courier Corporation |
| Total Pages | : 484 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 048613802X |
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
| Author | : Alexander L. Fetter |
| Publisher | : Courier Corporation |
| Total Pages | : 596 |
| Release | : 2003-12-16 |
| Genre | : Science |
| ISBN | : 0486432610 |
This two-part text fills what has often been a void in the first-year graduate physics curriculum. Through its examination of particles and continua, it supplies a lucid and self-contained account of classical mechanics — which in turn provides a natural framework for introducing many of the advanced mathematical concepts in physics. The text opens with Newton's laws of motion and systematically develops the dynamics of classical particles, with chapters on basic principles, rotating coordinate systems, lagrangian formalism, small oscillations, dynamics of rigid bodies, and hamiltonian formalism, including a brief discussion of the transition to quantum mechanics. This part of the book also considers examples of the limiting behavior of many particles, facilitating the eventual transition to a continuous medium. The second part deals with classical continua, including chapters on string membranes, sound waves, surface waves on nonviscous fluids, heat conduction, viscous fluids, and elastic media. Each of these self-contained chapters provides the relevant physical background and develops the appropriate mathematical techniques, and problems of varying difficulty appear throughout the text.
| Author | : Robert Weinstock |
| Publisher | : Courier Corporation |
| Total Pages | : 354 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486141063 |
This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society.
