Newtonian Dynamics

Front Cover
Contents
Preface
1. A Reveiw of Some Basics
	1.1 Qualitative Reasoning
	1.2 Vectors and the Scalar Product
	1.3 Tossing Rocks
		Tossing up the Hill
	1.4 A Consequence of Newton’s Second Law: Energy
		F and grad U
		Cartesian Representation
	1.5 Gravitational Potential Energy
	1.6 Potential Energy and Stability
	1.7 Some Implications of Invariance
		Translational Invariance
		Rotational Invariance
		Invariance under Time Translation
	1.8 Newton’s Laws: Structure and Meaning
	1.9 Reviewing the Review
	Worked Problems
	Problems
2. The Harmonic Oscillator
	2.1 Damped Harmonic Oscillator
		Damped Oscillations
		Energy
	2.2 Phase Space: An Introduction
	2.3 Harmonic Oscillation in Two Dimensions
	2.4 Sinusoidally Driven Oscillator
		The Lortentz Atom
	2.5 Quality Factor Q
	2.6 A Guide to the Major Ideas
	Worked Problems
	Problems
3. Nonlinear Oscillators
	3.1 A Nonlinear Oscillator
		Small Oscillations
		Phase Space Again
		Instability
		Summary of Principles
	3.2 Amplitude Jumps and Hysteresis
		Duffing’s Equation without Damping
	3.3 Van der Pol’s Equation: The Limit Cycle
	3.4 More Uses for the Averaging Method
		Newton’s Law of Damping
	3.5 Series Expansions
		Secular Terms
		A Note About Appearances
		Synopsis
	3.6 About the Methods
	Worked Problems
	Problems
4. Lagrangian Formulation
	4.1 Fermat’s Principle
	4.2 Calculus of Variations
		The Economical Lampshade
	4.3 Newton II as an Extremal Principle
		Newton II in Cylindrical Coordinates
	4.4 Lagrangians and Constraints
		Constraints
	4.5 Another Instance of Constrained Motion
		Equilibrium
		Interlude on Newton II
		Stability
	4.6 Conversion to First-Order Equations: Hamilton’s Equations
		Examples
		Examples Continued
		The Example Again
	4.7 Liouville’s Theorem*
	4.8 The Lagrangian and Quantum Mechanics
	4.9 A Sense of Perspective
	Worked Problem
	Problems
5. Two-Body Problem
	5.1 Reduction to Motion in a Plane
		Plane Polar Coordinates
	5.2 Effective Potential Energy
		Gravitational Attraction
		Spring Force
	5.3 Orbit Shape
	5.4 Orbits Around the Spherical Sun
		The Typical Bound Orbit
		Classifying the Objects
	5.5 The Oblate Sun
	5.6 Stability of Circular Orbits
		How a Pertubation Evolves in Time
		Stability Criteria
	5.7 The Orbit in Time
	5.8 Compendium on Central-Force Motion
	Worked Problems
	Problems
6. Rotating Frames of Reference
	6.1 Vectors in a Rotating Frame of Reference
		Uniform Rotation
		General Rotation
		Illustration
		The Primary Derivation Resumed
	6.2 Physics on a Rotating Table
	6.3 The Rotating Earth
		The Plumb Bob
		Motion near the Earth’s Surface
		The Wind
	6.4 Foucault Pendulum
	6.5 The Figure of the Earth
		Geopotential
	6.6 A Perspectie on Rotating Frames
	Worked Problem
	Problems
7. Extended Bodies in Rotation
	7.1 Equations for Location and Orientation
		Equation for Location
		Equation for Orientation
		More about Torque
	7.2 Simple Precession
		The Dust Grain: An Example
	7.3 How L is Related to ω
		Familiar Ground
	7.4 A Novel Pendulum
		Fixed Axis of Rotation
	7.5 L is not Necessarily Parallell to ω
	7.6 Diagonal Form for the Inertia Tensor
	7.7 Euler’s Equations for a Rigid Body
	7.8 Axisymmetric and Torque-Free
		Evolution of ω
		Orientation of the Disk in Space
		ω as Seen from the Inertial Frame
		Summary
		The Dust Grain Again
	7.9 Chandler Wobble
	7.10 An Interlude on Kinetic Energy
	7.11 The Symmetric, Supported Top
		Conserved Quantities
		How the Top’s Orientation Changes
		Extracting the Implications
	7.12 Precession of the Equinoxes
	7.13 Survey of the Critical Notions
	Worked Problems
	Problems
8. Cross Sections
	8.1 Scattering Effectiveness: The Idea Behind the Cross Section
	8.2 A Capture Cross Section
	8.3 A Differential Cross Section
	8.4 Rutherford Scattering
	8.5 Major Ideas
	Worked Problems
	Problems
Appendices
	A. Expansions, Identities, and Miscellany
		A.1 Expansions
		A.2 Trigonometric Identities
		A.3 Miscellany
	B. Vector Product
		Components and Orthogonal Unit Vectors
		Some Identities
		A x B as an Axial Vector
	C. The Averaging Method
	D. The Craft of the Physicist
Index
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