Modern Introductory Mechanics
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740308556
Table of contents: title: Innhold; title: Chapter 1: Mathematical Review; title: Trigonometry; title: Matrices; title: Orthogonal Transformations; title: Scalar and Vector Fields; title: Vector Algebra and Scalar Differentiation; title: Alternate Coordinate Systems; title: Angular Velocity; title: Differential Operators and Leibnitz Rule; title: Complex Variables; title: Problems; title: Chapter 2: Newtonian Mechanics; title: Review of Newton’s Laws; title: Simple Examples using Newton’s Laws; title: Single Particle Conservation Theorems; title: Potential Energy and Particle Motion; title: Equilibrium and Stability in One Dimension; title: Equilibrium and Stability in D Dimensions; title: Problems; title: Chapter 3: Linear Oscillations; title: General Restoring Forces in One and Two Dimensions; title: Damped Oscillations; title: Circuit/Oscillator Analogy; title: Driven Harmonic Oscillations; title: Fourier Series Methods; title: Green Function Methods; title: Problems; title: Chapter 4: Nonlinear Oscillations; title: The Anharmonic Oscillator; title: The Plane Pendulum; title: Phase Diagrams and Nonlinear Oscillations; title: The Logistic Difference Equation; title: Fractals; title: Chaos in Physical Systems; title: Dissipative Phase Space; title: Lyapunov Exponents; title: The Intermittent Transition to Chaos; title: Problems; title: Chapter 5: Gravitation; title: Newton’s Law of Gravitation; title: Gravitational Potential; title: Modifications for Extended Objects; title: Eötvös Experiment on Composition Dependence of...; title: Gravitational Forces; title: Problems; title: Chapter 6: Calculus of Variations; title: Euler-Lagrange Equation; title: “Second form” of Euler’s Equation; title: Brachistochrone Problem; title: The Case of More than One Dependent Variable; title: The Case of More than One Independent Variable; title: Constraints; title: Lagrange Multipliers; title: Isoperimetric Problems; title: Variation of the End Points of Integration; title: Problems; title: Chapter 7: Lagrangian and Hamiltonian Mechanics; title: The Action and Hamilton's Principle; title: Generalized Coordinates; title: Examples of the Formalism; title: Two Points about Lagrangian Methods; title: Types of Constraints; title: Endpoint Invariance: Multiparticle Conservation Laws; title: Consequences of Scale Invariance; title: When Does H=T+U?; title: Investigation into the Meaning of...; title: Hamilton’s Equations; title: Holonomic Constraints in Hamiltonian Formalism; title: Problems