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Bibliografická citace

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0 (hodnocen0 x )
BK
Singapore : World Scientific, c2014
xv, 574 s. : il. ; 24 cm

objednat
ISBN 978-981-4551-48-9 (váz.)
Obsahuje bibliografii na s. 561-563 a rejstřík
000250043
Contents // Preface // 1 Vectors, Tensors, and Linear Transformations // 2 Exterior Algebra: Determinants, Oriented Frames and Oriented Volumes // 3 The Hodge-Star Operator and the Vector Cross Product // 4 Kinematics and Moving Frames: // From the Angular Velocity to Gauge Fields // 5 Differentiable Manifolds: // The Tangent and Cotangent Bundles // 6 Exterior Calculus: Differential Forms // 7 Vector Calculus by Differential Forms // 8 The Stokes Theorem // 9 Cartan’s Method of Moving Frames: // Curvilinear Coordinates in R3 // 10 Mechanical Constraints: The Frobenius Theorem // 11 Flows and Lie Derivatives // 12 Newton’s Laws: Inertial and Non-inertial Frames // 13 Simple Applications of Newton’s Laws // 14 Potential Theory: Newtonian Gravitation // 15 Centrifugal and Coriolis Forces // xiii // vii // 1 // 19 // 33 // 41 // 53 // 63 // 73 // 77 // 91 // 103 // 109 // 117 // 127 // 147 // 163 // XIV // Fundamental Principles of Classical Mechanics // 16 Harmonic Oscillators: Fourier Transforms and // Green’s Functions 171 // 17 Classical Model of the Atom: Power Spectra 183 // 18 Dynamical Systems and their Stabilities 191 // 19 Many-Particle Systems and the Conservation Principles 209 // 20 Rigid-Body Dynamics: // The Euler-Poisson Equations of Motion 217 // 21 Topology and Systems with Holonomic Constraints: // Homology and de Rham Cohomology 231 // 22 Connections on Vector Bundles: // Affine Connections on Tangent Bundles 241 // 23 The Parallel Translation of Vectors:
The Foucault Pendulum 253 // 24 Geometric Phases, Gauge Fields, and the Mechanics of // Deformable Bodies: The “Falling Cat” Problem 261 // 25 Force and Curvature 273 // 26 The Gauss-Bonnet-Chern Theorem and Holonomy 291 // 27 The Curvature Tensor in Riemannian Geometry 299 // 28 Frame Bundles and Principal Bundles, // Connections on Principal Bundles 317 // 29 Calculus of Variations, the Euler-Lagrange Equations, // the First Variation of Arclength and Geodesics 329 // 30 The Second Variation of Arclength, Index Forms, and // Jacobi Fields 345 // 31 The Lagrangian Formulation of Classical Mechanics: // Hamilton’s Principle of Least Action, Lagrange // Multipliers in Constrained Motion 357 // 32 Small Oscillations and Normal Modes 367 // 33 The Hamiltonian Formulation of Classical Mechanics: // Hamilton’s Equations of Motion 381 // Contents // XV // 34 Symmetry and Conservation 399 // 35 Symmetric Tops 403 // 36 Canonical Transformations and the Symplectic Group 411 // 37 Generating Functions and the Hamilton-Jacobi Equation 423 // 38 Integrability, Invariant Tori, Action-Angle Variables 445 // 39 Symplectic Geometry in Hamiltonian Dynamics, // Hamiltonian Flows, and Poincaré-Cartan // Integral Invariants 467 // 40 Darboux’s Theorem in Symplectic Geometry 479 // 41 The Kolmogorov-Arnold-Moser (KAM) Theorem 487 // 42 The Homoclinic Tangle and Instability, Shifts as Subsystems 521 // 43 The Restricted Three-Body Problem 547 // References 561 // Index // 565

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