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Classical mechanics /
Kinematics: Describing the MotionIntroductionSpace, Time, and Coordinate SystemsChange of Coordinate System (Transformation of Components of a Vector)Displacement VectorSpeed and VelocityAccelerationVelocity and Acceleration in Polar CoordinatesAngular Velocity and Angular AccelerationInfinitesimal...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Place of publication not identified] :
CRC Press,
2013.
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| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Kinematics: Describing the Motion; Introduction; Space, Time, and Coordinate Systems; Change of Coordinate System (Transformation of Components of a Vector); Displacement Vector; Speed and Velocity; Acceleration; Velocity and Acceleration in Polar Coordinates; Angular Velocity and Angular Acceleration; Infinitesimal Rotations and the Angular Velocity Vector; ; Newtonian Mechanics; The First Law of Motion (Law of Inertia); The Second Law of Motion; the Equations of Motion; The Third Law of Motion; Galilean Transformations and Galilean Invariance; Newton's Laws of Rotational Motion; Work, Energy,
- And Conservation Laws; Systems of Particles; References; ; Integration of Newton's Equation of Motion; Introduction; Motion Under Constant Force; Force Is a Function of Time; Force Is a Function of Velocity; Force Is a Function of Position; Time-Varying Mass System (Rocket System); ; Lagrangian Formulation of Mechanics: Descriptions of Motion in Configuration Space; Generalized Coordinates and Constraints; Kinetic Energy in Generalized Coordinates; Generalized Momentum; Lagrangian Equations of Motion; Nonuniqueness of the Lagrangian; Integrals of Motion and Conservation Laws; Scale Invariance; Nonconservative Systems and Generalized Potential; Charged Particle in Electromagnetic Field; Forces of Constraint and Lagrange's Multipliers; Lagrangian versus Newtonian Approach to Classical Mechanics; Reference; ; Hamiltonian Formulation of Mechanics: Descriptions of Motion in PhaseSpaces; The Hamiltonian of a.
- Dynamic System; Hamilton's Equations of Motion; Integrals of Motion and Conservation Theorems; Canonical Transformations; Poisson Brackets; Poisson Brackets and Quantum Mechanics; Phase Space and Liouville's Theorem; Time Reversal in Mechanics (Optional); Passage from Hamiltonian to Lagrangian; References; ; Motion Under a Central Force; Two-Body Problem and Reduced Mass; General Properties of Central Force Motion; Effective Potential and Classification of Orbits; General Solutions of Central Force Problem; Inverse Square Law of Force; Kepler's Three Laws of Planetary Motion; Applications of Central Force Motion; Newton's Law of Gravity from Kepler's Laws; Stability of Circular Orbits (Optional); Apsides and Advance of Perihelion (Optional); Laplace-Runge-Lenz Vector and the Kepler Orbit (Optional); References; ; Harmonic Oscillator; Simple Harmonic Oscillator; Adiabatic Invariants and Quantum.
- Condition; Damped Harmonic Oscillator; Phase Diagram for Damped Oscillator; Relaxation Time Phenomena; Forced Oscillations without Damping; Forced Oscillations with Damping; Oscillator Under Arbitrary Periodic Force; Vibration Isolation; Parametric Excitation; ; Coupled Oscillations and Normal Coordinates; Coupled Pendulum; Coupled Oscillators and Normal Modes: General Analytic Approach; Forced Oscillations of Coupled Oscillators; Coupled Electric Circuits; ; Nonlinear Oscillations; Qualitative Analysis: Energy and Phase Diagrams; Elliptical Integrals and Nonlinear Oscillations; Fourier Series Expansions; The Method of Perturbation; Ritz Method; Method of Successive Approximation; Multiple Solutions and Jumps; Chaotic Oscillations; References; ; Collisions and Scatterings; Direct Impact of Two Particles; Scattering Cross Sections and Rutherford Scattering; Laboratory and Center-of-Mass Frames of.
- Reference; Nuclear Sizes; Small-Angle Scattering (Optional); References; ; Motion in Non-Inertial Systems; Accelerated Translational Coordinate System; Dynamics in Rotating Coordinate System; Motion of Particle Near the Surface of the Earth; Foucault Pendulum; Larmor's Theorem; Classical Zeeman Effect; Principle of Equivalence; ; Motion of Rigid Bodies; Independent Coordinates of Rigid Body; Eulerian Angles; Rate of Change of Vector; Rotational Kinetic Energy and Angular Momentum; Inertia Tensor; Euler's Equations of Motion; Motion of a Torque-Free Symmetrical Top; Motion of Heavy Symmetrical Top with One Point Fixed; Stability of Rotational Motion; References; ; Theory of Special Relativity; Historical Origin of Special Theory of Relativity; Michelson-Morley Experiment; Postulates of Special Theory of Relativity; Lorentz Transformations; Doppler Effect; Relativistic Space-Time (Minkowski.
- Space); Equivalence of Mass and Energy; Conservation Laws of Energy and Momentum; Generalization of Newton's Equation of Motion; Relativistic Lagrangian and Hamiltonian Functions; Relativistic Kinematics of Collisions; Collision Threshold Energies; References; ; Newtonian Gravity and Newtonian Cosmology; Newton's Law of Gravity; Gravitational Field and Gravitational Potential; Gravitational Field Equations: Poisson's and Laplace's Equations; Gravitational Field and Potential of Extended Body; Tides; General Theory of Relativity: Relativistic Theory of Gravitation; Introduction to Cosmology; Brief History of Cosmological Ideas; Discovery of Expansion of the Universe,
- Hubble's Law; Big Bang; Formulating Dynamical Models of the Universe; Cosmological Red Shift and Hubble Constant H ; Critical Mass Density and Future of the Universe; Microwave Background Radiation; Dark Matter; Reference; ; Hamilton-Jacobi Theory of Dynamics; Canonical Transformation and H-J Equation; Action and Angle Variables; Infinitesimal Canonical Transformations and Time Development Operator; H-J Theory and Wave Mechanics; Reference; ; Introduction to Lagrangian and Hamiltonian Formulations for Continuous Systems and Classical Fields; Vibration of Loaded String; Vibrating Strings and the Wave Equation; Continuous Systems and Classical Fields; Scalar and Vector of Fields; ; Appendix 1: Vector Analysis and Ordinary Differential Equations; Appendix 2: D'Alembert's Principle and Lagrange's Equations; Appendix 3: Derivation of Hamilton's Principle from D'Alembert's Principle; Appendix 4.
- Noether's Theorem; Appendix 5: Conic Sections, Ellipse, Parabola, and Hyperbola; ; Index.