Author | : V.I. Arnol'd |

Publisher | : Springer Science & Business Media |

Release Date | : 2013-04-09 |

ISBN 10 | : 1475720637 |

Pages | : 520 pages |

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 | : Henri Gouin |

Publisher | : Elsevier |

Release Date | : 2020-11-27 |

ISBN 10 | : 0128229861 |

Pages | : 320 pages |

Mathematical Methods of Analytical Mechanics uses tensor geometry and geometry of variation calculation, includes the properties associated with Noether's theorem, and highlights methods of integration, including Jacobi's method, which is deduced. In addition, the book covers the Maupertuis principle that looks at the conservation of energy of material systems and how it leads to quantum mechanics. Finally, the book deduces the various spaces underlying the analytical mechanics which lead to the Poisson algebra and the symplectic geometry. Helps readers understand calculations surrounding the geometry of the tensor and the geometry of the calculation of the variation Presents principles that correspond to the energy conservation of material systems Defines the invariance properties associated with Noether's theorem Discusses phase space and Liouville's theorem Identifies small movements and different types of stabilities

Author | : V. I. Arnold |

Publisher | : Springer Science & Business Media |

Release Date | : 2013-11-11 |

ISBN 10 | : 1475716931 |

Pages | : 464 pages |

Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.

Author | : M. de León,P.R. Rodrigues |

Publisher | : Elsevier |

Release Date | : 2011-08-18 |

ISBN 10 | : 9780080872698 |

Pages | : 482 pages |

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint. Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

Author | : V.I. Arnol'd |

Publisher | : Springer |

Release Date | : 1997-09-05 |

ISBN 10 | : 9780387968902 |

Pages | : 520 pages |

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 | : Ioan Merches,Daniel Radu |

Publisher | : CRC Press |

Release Date | : 2014-08-26 |

ISBN 10 | : 148223940X |

Pages | : 456 pages |

Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive a

Author | : Nivaldo A. Lemos |

Publisher | : Cambridge University Press |

Release Date | : 2018-08-09 |

ISBN 10 | : 1108416586 |

Pages | : 470 pages |

An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

Author | : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt |

Publisher | : Springer Science & Business Media |

Release Date | : 2007-07-05 |

ISBN 10 | : 3540489266 |

Pages | : 505 pages |

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Author | : John L. Bohn |

Publisher | : Cambridge University Press |

Release Date | : 2018-09-30 |

ISBN 10 | : 1107145767 |

Pages | : 226 pages |

An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.

Author | : John G. Papastavridis |

Publisher | : World Scientific Publishing Company Incorporated |

Release Date | : 2014 |

ISBN 10 | : 9789814338714 |

Pages | : 1392 pages |

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.

Author | : Louis N. Hand,Janet D. Finch |

Publisher | : Cambridge University Press |

Release Date | : 1998-11-13 |

ISBN 10 | : 1139643312 |

Pages | : 329 pages |

Analytical Mechanics, first published in 1999, provides a detailed introduction to the key analytical techniques of classical mechanics, one of the cornerstones of physics. It deals with all the important subjects encountered in an undergraduate course and prepares the reader thoroughly for further study at graduate level. The authors set out the fundamentals of Lagrangian and Hamiltonian mechanics early on in the book and go on to cover such topics as linear oscillators, planetary orbits, rigid-body motion, small vibrations, nonlinear dynamics, chaos, and special relativity. A special feature is the inclusion of many 'e-mail questions', which are intended to facilitate dialogue between the student and instructor. Many worked examples are given, and there are 250 homework exercises to help students gain confidence and proficiency in problem-solving. It is an ideal textbook for undergraduate courses in classical mechanics, and provides a sound foundation for graduate study.

Author | : Frederick W. Byron,Robert W. Fuller |

Publisher | : Courier Corporation |

Release Date | : 2012-04-26 |

ISBN 10 | : 0486135063 |

Pages | : 672 pages |

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.