# Mathematical Methods of Analytical Mechanics Books

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## Mathematical Methods of Analytical Mechanics

- Author : Henri Gouin
- Publisher : Elsevier
- Release : 2020-11-27
- ISBN : 9780128229866
- Language : En, Es, Fr & De

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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

## Mathematical Methods of Classical Mechanics

- Author : V. I. Arnold
- Publisher : Springer Science & Business Media
- Release : 2013-11-11
- ISBN : 9781475716931
- Language : En, Es, Fr & De

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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.

## Mathematical Methods of Classical Mechanics

- Author : V.I. Arnol'd
- Publisher : Springer
- Release : 1997-09-05
- ISBN : 0387968903
- Language : En, Es, Fr & De

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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.

## Mathematical Methods of Classical Mechanics

- Author : V. I. Arnold
- Publisher : Springer
- Release : 1984-07-30
- ISBN : 0387903143
- Language : En, Es, Fr & De

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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.

## Methods of Differential Geometry in Analytical Mechanics

- Author : M. de León
- Publisher : Elsevier
- Release : 2011-08-18
- ISBN : 0080872697
- Language : En, Es, Fr & De

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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.