Modern Introductory Mechanics
Publisher: Bookboon.com
Published: 2015
ISBN-13: 9788740308556
Table of contents: title: Indholdsfortegnelse; title: 1. Chapter 1: Mathematical Review; title: 1.1. Trigonometry; title: 1.2. Matrices; title: 1.3. Orthogonal Transformations; title: 1.4. Scalar and Vector Fields; title: 1.5. Vector Algebra and Scalar Differentiation; title: 1.6. Alternate Coordinate Systems; title: 1.7. Angular Velocity; title: 1.8. Differential Operators and Leibnitz Rule; title: 1.9. Complex Variables; title: 1.10. Problems; title: 2. Chapter 2: Newtonian Mechanics; title: 2.1. Review of Newton’s Laws; title: 2.2. Simple Examples using Newton’s Laws; title: 2.3. Single Particle Conservation Theorems; title: 2.4. Potential Energy and Particle Motion; title: 2.5. Equilibrium and Stability in One Dimension; title: 2.6. Equilibrium and Stability in D Dimensions; title: 3. Problems; title: 3.1. Chapter 3: Linear Oscillations; title: 3.2. General Restoring Forces in One and Two Dimensions; title: 3.3. Damped Oscillations; title: 3.4. Circuit/Oscillator Analogy; title: 3.5. Driven Harmonic Oscillations; title: 3.6. Fourier Series Methods; title: 3.7. Green Function Methods; title: 3.8. Problems; title: 4. Chapter 4: Nonlinear Oscillations; title: 4.1. The Anharmonic Oscillator; title: 4.2. The Plane Pendulum; title: 4.3. Phase Diagrams and Nonlinear Oscillations; title: 4.4. The Logistic Difference Equation; title: 4.5. Fractals; title: 4.6. Chaos in Physical Systems; title: 4.7. Dissipative Phase Space; title: 4.8. Lyapunov Exponents; title: 4.9. The Intermittent Transition to Chaos; title: 4.10. Problems; title: 5. Chapter 5: Gravitation; title: 5.1. Newton’s Law of Gravitation; title: 5.2. Gravitational Potential; title: 5.3. Modifications for Extended Objects; title: 5.4. Eötvös Experiment on Composition Dependence of...; title: 5.5. Gravitational Forces; title: 5.6. Problems; title: 6. Chapter 6: Calculus of Variations; title: 6.1. Euler-Lagrange Equation; title: 6.2. “Second form” of Euler’s Equation; title: 6.3. Brachistochrone Problem; title: 6.4. The Case of More than One Dependent Variable; title: 6.5. The Case of More than One Independent Variable; title: 6.6. Constraints; title: 6.7. Lagrange Multipliers; title: 6.8. Isoperimetric Problems; title: 6.9. Variation of the End Points of Integration; title: 6.10. Problems; title: 7. Chapter 7: Lagrangian and Hamiltonian Mechanics; title: 7.1. The Action and Hamilton's Principle; title: 7.2. Generalized Coordinates; title: 7.3. Examples of the Formalism; title: 7.4. Two Points about Lagrangian Methods; title: 7.5. Types of Constraints; title: 7.6. Endpoint Invariance: Multiparticle Conservation Laws; title: 7.7. Consequences of Scale Invariance; title: 7.8. When Does H=T+U?; title: 7.9. Investigation into the Meaning of...; title: 7.10. Hamilton’s Equations; title: 7.11. Holonomic Constraints in Hamiltonian Formalism; title: 7.12. Problems