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Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course)

Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course) Summary:

A complete set of lecture notes for an upper-division undergraduate Newtonian dynamics course. The course concentrates on those aspects of classical dynamics which can be studied analytically. Topics covered include oscillations, Keplerian orbits, two-body scattering, rotating frames of reference, rotation of rigid bodies in three dimensions, Lagrangian mechanics, Hamiltonian mechanics, and coupled oscillations.

Introduction
- Prerequisites
- Scope of Book
- Major Sources
Vector Algebra and Vector Calculus
- Introduction
- Vector Algebra
- Scalar Product
- Vector Product
- Rotation
- Scalar Triple Product
- Vector Triple Product
- Vector Calculus
- Line Integrals
- Vector Line Integrals
- Volume Integrals
- Gradient
- Exercises
Fundamental Concepts
- Introduction
- Fundamental Assumptions
- Newton's Laws of Motion
- Newton's First Law of Motion
- Newton's Second Law of Motion
- Newton's Third Law of Motion
- Exercises
One-Dimensional Motion
- Introduction
- Motion in a General One-Dimensional Potential
- Velocity Dependent Forces
- Simple Harmonic Motion
- Damped Oscillatory Motion
- Quality Factor
- Resonance
- Periodic Driving Forces
- Transients
- Simple Pendulum
- Exercises
Multi-Dimensional Motion
- Introduction
- Motion in a Two-Dimensional Harmonic Potential
- Projectile Motion with Air Resistance
- Charged Particle Motion in Electric and Magnetic Fields
- Exercises
Planetary Motion
- Introduction
- Kepler's Laws
- Newtonian Gravity
- Conservation Laws
- Plane Polar Coordinates
- Conic Sections
- Kepler's Second Law
- Kepler's First Law
- Kepler's Third Law
- Orbital Energies
- Kepler Problem
- Motion in a General Central Force-Field
- Motion in a Nearly Circular Orbit
- Exercises
Two-Body Dynamics
- Introduction
- Reduced Mass
- Binary Star Systems
- Scattering in the Center of Mass Frame
- Scattering in the Laboratory Frame
- Exercises
Non-Inertial Reference Frames
- Introduction
- Rotating Reference Frames
- Centrifugal Acceleration
- Coriolis Force
- Foucault Pendulum
- Exercises
Rigid Body Rotation
- Introduction
- Fundamental Equations
- Moment of Inertia Tensor
- Rotational Kinetic Energy
- Matrix Eigenvalue Theory
- Principal Axes of Rotation
- Euler's Equations
- Eulerian Angles
- Gyroscopic Precession
- Rotational Stability
- Exercises
Lagrangian Dynamics
- Introduction
- Generalized Coordinates
- Generalized Forces
- Lagrange's Equation
- Motion in a Central Potential
- Atwood Machines
- Sliding down a Sliding Plane
- Generalized Momenta
- Spherical Pendulum
- Exercises
Hamiltonian Dynamics
- Introduction
- Calculus of Variations
- Conditional Variation
- Multi-Function Variation
- Hamilton's Principle
- Constrained Lagrangian Dynamics
- Hamilton's Equations
- Exercises
Coupled Oscillations
- Introduction
- Equilibrium State
- Stability Equations
- More Matrix Eigenvalue Theory
- Normal Modes
- Normal Coordinates
- Spring-Coupled Masses
- Triatomic Molecule
- Exercises
Gravitational Potential Theory
- Introduction
- Gravitational Potential
- Axially Symmetric Mass Distributions
- Potential Due to a Uniform Sphere
- Potential Outside a Uniform Spheroid
- Rotational Flattening
- McCullough's Formula
- Tidal Elongation
- Roche Radius
- Precession of the Equinoxes
- Potential Due to a Uniform Ring
- Perihelion Precession of the Planets
- Perihelion Precession of Mercury
- Exercises
The Three-Body Problem
- Introduction
- Circular Restricted Three-Body Problem
- Jacobi Integral
- Tisserand Criterion
- Co-Rotating Frame
- Lagrange Points
- Zero-Velocity Surfaces
- Stability of Lagrange Points
The Chaotic Pendulum
- Introduction
- Basic Problem
- Analytic Solution
- Numerical Solution
- Poincaré Section
- Spatial Symmetry Breaking
- Basins of Attraction
- Period-Doubling Bifurcations
- Route to Chaos
- Sensitivity to Initial Conditions
- Definition of Chaos
- Periodic Windows
- Further Investigation

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Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course) Keywords

potential dynamics vector kepler rotation precession newton equations pendulum newtonian lagrangian calculus theory fundamental forces coordinates uniform frame newtonian dynamics introduction fundamental pendulum exercises vector algebra dynamics introduction vector calculus reference frames lecture notes undergraduate newtonian upper division undergraduate undergraduate newtonian dynamics upper division undergraduate newtonian

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Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course)

Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course)

Newtonian Dynamics (Lecture Notes for an upper-division undergraduate Newtonian dynamics course) Summary:

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