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|a 1224957114
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|a 9780128229866
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|a 0128229861
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|z (OCoLC)1224957114
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|a 531.01515
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|a Gouin, Henri.
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|a Mathematical Methods of Analytical Mechanics
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|a San Diego :
|b ISTE Press Ltd. :
|b Elsevier,
|c 2020.
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|a 1 online resource (322 pages)
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
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|a Print version record.
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|a Front Cover -- Introduction to Mathematical Methods of Analytical Mechanics -- Copyright Page -- Contents -- Preface -- Mathematicians, Physicists and Astronomers Cited in this Book -- Important Notations -- PART 1: Introduction to the Calculus of Variations -- 1. Elementary Methods to the Calculus of Variations -- 1.1. First free extremum problems -- 1.2. First constrained extremum problem -- Lagrange multipliers -- 1.3. The fundamental lemma of the calculus of variations -- 1.4. Extremum of a free functional -- 1.5. Extremum for a constrained functional
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|a 1.6. More general problem of the calculus of variations -- 2. Variation of Curvilinear Integral -- 2.1. Geometrization of variational problems -- 2.2. First form of curvilinear integral -- 2.3. Second form of curvilinear integrals -- 2.4. Generalization and variation of derivative -- 2.5. First application: studying the optical path of light -- 2.6. Second application: the problem of isoperimeters -- 3. The Noether Theorem -- 3.1. Additional results on differential equations -- 3.2. One-parameter groups and Lie groups -- 3.3. Invariant integral under a Lie group
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|a 3.4. Further examination of Fermat's principle -- PART 2: Applications to Analytical Mechanics -- 4. The Methods of Analytical Mechanics -- 4.1. D'Alembert's principle -- 4.2. Back to analytical mechanics -- 4.3. The vibrating strings -- 4.4. Homogeneous Lagrangian. Expression in space time -- 4.5. The Hamilton equations -- 4.6. First integral by using the Noether theorem -- 4.7. Re-injection of a partial result -- 4.8. The Maupertuis principle -- 5. Jacobi's Integration Method -- 5.1. Canonical transformations -- 5.2. The Jacobi method
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|a 5.3. The material point in various systems of representation -- 5.4. Case of the Liouville integrability -- 5.5. A specific change of canonical variables -- 5.6. Multi-periodic systems. Action variables -- 6. Spaces of Mechanics -- Poisson Brackets -- 6.1. Spaces in analytical mechanics -- 6.2. Dynamical variables -- Poisson brackets -- 6.3. Poisson bracket of two dynamical variables -- 6.4. Canonical transformations -- 6.5. Remark on the symplectic scalar product -- PART 3: Properties of Mechanical Systems -- 7. Properties of Phase Space -- 7.1. Flow of a dynamical system
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|a 7.2. The Liouville theorem -- 7.3. The Poincar�e recurrence theorem -- 8. Oscillations and Small Motions of Mechanical Systems -- 8.1. Preliminary remarks -- 8.2. The Weierstrass discussion -- 8.3. Equilibrium position of an autonomous differential equation -- 8.4. Stability of equilibrium positions of an autonomous differential equation -- 8.5. A necessary condition of stability -- 8.6. Linearization of a differential equation -- 8.7. Behavior of eigenfrequencies -- 8.8. Perturbed equation associated with linear differential equation -- 9. The Stability of Periodic Systems
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| 650 |
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|a Mechanics, Analytic
|x Mathematics.
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| 650 |
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|a M�ecanique analytique
|0 (CaQQLa)201-0023814
|x Math�ematiques.
|0 (CaQQLa)201-0380112
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| 776 |
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|i Print version:
|a Gouin, Henri.
|t Mathematical Methods of Analytical Mechanics.
|d San Diego : ISTE Press Limited - Elsevier Incorporated, �2020
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| 856 |
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|u https://sciencedirect.uam.elogim.com/science/book/9781785483158
|z Texto completo
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