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E-grāmata: Analytical Mechanics

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  • Formāts: EPUB+DRM
  • Izdošanas datums: 09-Aug-2018
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108265942
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Analytical MechanicsPalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 09-Aug-2018
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108265942
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"Analytical Mechanics is the foundation of many areas of theoretical physics including quantum theory and statistical mechanics, and has wide-ranging applications in engineering and celestial mechanics. This introduction to the basic principles and methods of analytical mechanics covers Lagrangian and Hamiltonian dynamics, rigid bodies, small oscillations, canonical transformations and Hamilton-Jacobi theory. This fully up-to-date textbook includes detailed mathematical appendices and addresses a number of advanced topics, some of them of a geometric or topological character. These include Bertrand's theorem, proof that action is least, spontaneous symmetry breakdown, constrained Hamiltonian systems, non-integrability criteria, KAM theory, classical field theory, Lyapunov functions, geometric phases and Poisson manifolds. Providing worked examples, end-of-chapter problems, and discussion of ongoing research in the field, it is suitable for advanced undergraduate students and graduate students studying analytical mechanics"--

Recenzijas

'The greatest strength of the book is that it starts with minimal knowledge and then takes the student very carefully into the modern concepts. The background required is a basic knowledge in classical dynamics and differential equations, with the other usual basic mathematics courses. By the end of the book the student is prepared for the advanced topics of modern geometric mechanics I highly recommend this book as an advanced undergraduate text in mathematics, physics or engineering.' Thomas J. Bridges, Contemporary Physics 'The contents cover the most relevant topics for an advanced undergraduate course on analytical mechanics, enlarged by a selection of topics of interest for graduate students and researchers. The chapter structure and subject sequence is carefully chosen, rendering a constructive and pedagogical approach.' Cesar Rodrigo, MathsSciNet

Papildus informācija

An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.
Preface xi
1 Lagrangian Dynamics
1(41)
1.1 Principles of Newtonian Mechanics
1(6)
1.2 Constraints
7(4)
1.3 Virtual Displacements and d'Alembert's Principle
11(6)
1.4 Generalised Coordinates and Lagrange's Equations
17(7)
1.5 Applications of Lagrange's Equations
24(4)
1.6 Generalised Potentials and Dissipation Function
28(3)
1.7 Central Forces and Bertrand's Theorem
31(11)
Problems
37(5)
2 Hamilton's Variational Principle
42(44)
2.1 Rudiments of the Calculus of Variations
42(7)
2.2 Variational Notation
49(1)
2.3 Hamilton's Principle and Lagrange's Equations
50(6)
2.4 Hamilton's Principle in the Non-Holonomic Case
56(9)
2.5 Symmetry Properties and Conservation Laws
65(6)
2.6 Conservation of Energy
71(2)
2.7 Noether's Theorem
73(13)
Problems
78(8)
3 Kinematics of Rotational Motion
86(26)
3.1 Orthogonal Transformations
86(6)
3.2 Possible Displacements of a Rigid Body
92(3)
3.3 Euler Angles
95(1)
3.4 Infinitesimal Rotations and Angular Velocity
96(6)
3.5 Rotation Group and Infinitesimal Generators
102(1)
3.6 Dynamics in Non-Inertial Reference Frames
103(9)
Problems
109(3)
4 Dynamics of Rigid Bodies
112(37)
4.1 Angular Momentum and Inertia Tensor
112(2)
4.2 Mathematical Interlude: Tensors and Dyadics
114(5)
4.3 Moments and Products of Inertia
119(1)
4.4 Kinetic Energy and Parallel Axis Theorem
120(2)
4.5 Diagonalisation of the Inertia Tensor
122(4)
4.6 Symmetries and Principal Axes of Inertia
126(3)
4.7 Rolling Coin
129(2)
4.8 Euler's Equations and Free Rotation
131(8)
4.9 Symmetric Top with One Point Fixed
139(10)
Problems
145(4)
5 Small Oscillations
149(34)
5.1 One-Dimensional Case
149(5)
5.2 Anomalous Case: Quartic Oscillator
154(7)
5.3 Stationary Motion and Small Oscillations
161(2)
5.4 Small Oscillations: General Case
163(2)
5.5 Normal Modes of Vibration
165(5)
5.6 Normal Coordinates
170(6)
5.7 Mathematical Supplement
176(7)
Problems
178(5)
6 Relativistic Mechanics
183(32)
6.1 Lorentz Transformations
183(5)
6.2 Light Cone and Causality
188(3)
6.3 Vectors and Tensors
191(3)
6.4 Tensor Fields
194(2)
6.5 Physical Laws in Covariant Form
196(3)
6.6 Relativistic Dynamics
199(5)
6.7 Relativistic Collisions
204(3)
6.8 Relativistic Dynamics in Lagrangian Form
207(2)
6.9 Action at a Distance in Special Relativity
209(6)
Problems
211(4)
7 Hamiltonian Dynamics
215(27)
7.1 Hamilton's Canonical Equations
215(5)
7.2 Symmetries and Conservation Laws
220(1)
7.3 The Virial Theorem
221(3)
7.4 Relativistic Hamiltonian Formulation
224(2)
7.5 Hamilton's Equations in Variational Form
226(2)
7.6 Time as a Canonical Variable
228(6)
7.7 The Principle of Maupertuis
234(8)
Problems
237(5)
8 Canonical Transformations
242(46)
8.1 Canonical Transformations and Generating Functions
242(6)
8.2 Canonicity and Lagrange Brackets
248(2)
8.3 Symplectic Notation
250(4)
8.4 Poisson Brackets
254(4)
8.5 Infinitesimal Canonical Transformations
258(4)
8.6 Angular Momentum Poisson Brackets
262(2)
8.7 Lie Series and Finite Canonical Transformations
264(4)
8.8 Theorems of Liouville and Poincare
268(4)
8.9 Constrained Hamiltonian Systems
272(16)
Problems
281(7)
9 The Hamilton-Jacobi Theory
288(50)
9.1 The Hamilton-Jacobi Equation
288(3)
9.2 One-Dimensional Examples
291(3)
9.3 Separation of Variables
294(5)
9.4 Incompleteness of the Theory: Point Charge in Dipole Field
299(4)
9.5 Action as a Function of the Coordinates
303(3)
9.6 Action-Angle Variables
306(6)
9.7 Integrable Systems: The Liouville-Arnold Theorem
312(4)
9.8 Non-integrability Criteria
316(2)
9.9 Integrability, Chaos, Determinism and Ergodicity
318(2)
9.10 Prelude to the KAM Theorem
320(3)
9.11 Action Variables in the Kepler Problem
323(2)
9.12 Adiabatic Invariants
325(4)
9.13 Hamilton-Jacobi Theory and Quantum Mechanics
329(9)
Problems
332(6)
10 Hamiltonian Perturbation Theory
338(22)
10.1 Statement of the Problem
338(3)
10.2 Generating Function Method
341(1)
10.3 One Degree of Freedom
342(3)
10.4 Several Degrees of Freedom
345(3)
10.5 The Kolmogorov-Arnold-Moser Theory
348(5)
10.6 Stability: Eternal or Long Term
353(1)
10.7 Lie Series Method
354(6)
Problems
358(2)
11 Classical Field Theory
360(32)
11.1 Lagrangian Field Theory
360(5)
11.2 Relativistic Field Theories
365(2)
11.3 Functional Derivatives
367(4)
11.4 Hamiltonian Field Theory
371(3)
11.5 Symmetries of the Action and Noether's Theorem
374(4)
11.6 Solitary Waves and Solitons
378(3)
11.7 Constrained Fields
381(11)
Problems
385(7)
Appendix A Indicial Notation 392(6)
Appendix B Frobenius Integrability Condition 398(8)
Appendix C Homogeneous Functions and Euler's Theorem 406(2)
Appendix D Vector Spaces and Linear Operators 408(13)
Appendix E Stability of Dynamical Systems 421(5)
Appendix F Exact Differentials 426(2)
Appendix G Geometric Phases 428(5)
Appendix H Poisson Manifolds 433(7)
Appendix I Decay Rate of Fourier Coefficients 440(2)
References 442(10)
Index 452
Nivaldo A. Lemos is Associate Professor of Physics at Universidade Federal Fluminense, Brazil. He was previously a visiting scholar at the Massachusetts Institute of Technology. His main research areas are quantum cosmology, quantum field theory and the teaching of classical mechanics.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97811082659426e.html
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