tailieunhanh - Ebook Classical mechanics: Part 1

(BQ) Part 1 book "Classical mechanics" has contents: Survey of elementary principles, variational principles and lagrange's equations, the central force problem, the kinematics of rigid body motion, the rigid body equations of motion, the rigid body equations of motion. | Sica MECHANICS CLASSICAL MECHANICS THIRD EDITION Herbert Goldstein Columbia University Charles Poole University of South Carolina John Safko University of South Carolina Addison Wesley San Francisco Bostor New York Capetown Hong Kong London Madrid Mexico City Montreal Munich Pans Singapore Sydney Tokyo Toronto Contents 1 Survey of the Elementary Principles 1 Mechanics of a Particle 1 Mechanics of a System of Particles 5 Constraints 12 1A D Alembert s Principle and Lagrange s Equations 16 Velocity-Dependent Potentials and the Dissipation Function 22 Simple Applications of the Lagrangian Formulation 24 2 Variational Principles and Lagrange s Equations 34 Hamilton s Principle 34 Some Techniques of the Calculus of Variations 36 Derivation of Lagrange s Equations from Hamilton s Principle 44 Extension of Hamilton s Principle to Nonholonomic Systems 45 Advantages of a Variational Principle Formulation 51 Conservation Theorems and Symmetry Properties 54 Energy Function and the Conservation of Energy 60 3 The Central Force Problem 70 Reduction to the Equivalent One-Body Problem 70 The Equations of Motion and First Integrals 72 The Equivalent One-Dimensional Problem and Classification of Orbits 76 The Virial Theorem 83 The Differential Equation for the Orbit and Integrable Power-Law Potentials 86 Conditions for Closed Orbits Bertrand s Theorem 89 The Kepler Problem Inverse-Square Law of Force 92 The Motion in Time in the Kepler Problem 98 The Laplace-Runge-Lenz Vector 102 Scattering in a Central Force Field 106 Transformation of the Scattering Problem to Laboratory Coordinates 114 The Three-Body Problem 121