File : pdf, 3.9 MB, 293 pages
TOC
1 Introduction
2 Vector Algebra and Vector Calculus
2.1 Introduction
2.2 Scalars and Vectors
2.3 Vector Algebra
2.4 Cartesian Components of a Vector
2.5 Coordinate Transformations
2.6 Scalar Product
2.7 Vector Product
2.8 Rotation
2.9 Scalar Triple Product
2.10 Vector Triple Product
2.11 Vector Calculus
2.12 Line Integrals
2.13 Vector Line Integrals
2.14 Volume Integrals
2.15 Gradient
2.16 Grad Operator
2.17 Polar Coordinates
3 Newton’s Laws of Motion
3.1 Introduction
3.2 Newtonian Dynamics
3.3 Newton’s Laws of Motion
3.4 Newton’s First Law of Motion
3.5 Newton’s Second Law of Motion
3.6 Newton’s Third Law of Motion
3.7 Non-Isolated Systems
4 One-Dimensional Motion
4.1 Introduction
4.2 Motion in a General One-Dimensional Potential
4.3 Velocity Dependent Forces
4.4 Simple Harmonic Motion
4.5 Damped Oscillatory Motion
4.6 Quality Factor
4.7 Resonance
4.8 Periodic Driving Forces
4.9 Transients
4.10 Simple Pendulum
5 Multi-Dimensional Motion
5.1 Introduction
5.2 Motion in a Two-Dimensional Harmonic Potential
5.3 Projectile Motion with Air Resistance
5.4 Charged Particle Motion in Electric and Magnetic Fields
6 Planetary Motion
6.1 Introduction
6.2 Kepler’s Laws
6.3 Newtonian Gravity
6.4 Conservation Laws
6.5 Plane Polar Coordinates
6.6 Conic Sections
6.7 Kepler’s Second Law
6.8 Kepler’s First Law
6.9 Kepler’s Third Law
6.10 Orbital Energies
6.11 Kepler Problem
6.12 Motion in a General Central Force-Field
6.13 Motion in a Nearly Circular Orbit
7 Two-Body Dynamics
7.1 Introduction
7.2 Reduced Mass
7.3 Binary Star Systems
7.4 Scattering in the Center of Mass Frame
7.5 Scattering in the Laboratory Frame
7.6 Exercises
8 Rotating Reference Frames
8.1 Introduction
8.2 Rotating Reference Frames
8.3 Centrifugal Acceleration
8.4 Coriolis Force
8.5 Foucault Pendulum
9 Rigid Body Rotation
9.1 Introduction
9.2 Fundamental Equations
9.3 Moment of Inertia Tensor
9.4 Rotational Kinetic Energy
9.5 Matrix Eigenvalue Theory
9.6 Principal Axes of Rotation
9.7 Euler’s Equations
9.8 Eulerian Angles
9.9 Gyroscopic Precession
9.10 Rotational Stability
10 Lagrangian Dynamics
10.1 Introduction
10.2 Generalized Coordinates
10.3 Generalized Forces
10.4 Lagrange’s Equation
10.5 Motion in a Central Potential
10.6 Atwood Machines
10.7 Sliding down a Sliding Plane
10.8 Generalized Momenta
10.9 Spherical Pendulum
10.10 Exercises
11 Hamiltonian Dynamics
11.1 Introduction
11.2 Calculus of Variations
11.3 Conditional Variation
11.4 Multi-Function Variation
11.5 Hamilton’s Principle
11.6 Constrained Lagrangian Dynamics
11.7 Hamilton’s Equations
12 Coupled Oscillations
12.1 Introduction
12.2 Equilibrium State
12.3 Stability Equations
12.4 More Matrix Eigenvalue Theory
12.5 Normal Modes
12.6 Normal Coordinates
12.7 Spring-Coupled Masses
12.8 Triatomic Molecule
13 Gravitational Potential Theory
13.1 Introduction
13.2 Gravitational Potential
13.3 Axially Symmetric Mass Distributions
13.4 Potential Due to a Uniform Sphere
13.5 Potential Outside a Uniform Spheroid
13.6 Rotational Flattening
13.7 McCullough’s Formula
13.8 Tidal Elongation
13.9 Roche Radius
13.10 Precession of the Equinoxes
13.11 Potential Due to a Uniform Ring
13.12 Perihelion Precession of the Planets
13.13 Perihelion Precession of Mercury
14 The Three-Body Problem
14.1 Introduction
14.2 Circular Restricted Three-Body Problem
14.3 Jacobi Integral
14.4 Tisserand Criterion
14.5 Co-Rotating Frame
14.6 Lagrange Points
14.7 Zero-Velocity Surfaces
14.8 Stability of Lagrange Points
15 Lunar Motion
15.1 Historical Background
15.2 Preliminary Analysis
15.3 Lunar Equations of Motion
15.4 Unperturbed Lunar Motion
15.5 Perturbed Lunar Motion
15.6 Description of Lunar Motion
16 The Chaotic Pendulum
16.1 Introduction
16.2 Basic Problem
16.3 Analytic Solution
16.4 Numerical Solution
16.5 Poincare Section
16.6 Spatial Symmetry Breaking
16.7 Basins of Attraction
16.8 Period-Doubling Bifurcations
16.9 Route to Chaos
16.10 Sensitivity to Initial Conditions
16.11 Definition of Chaos
16.12 Periodic Windows
16.13 Further Investigation
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