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by Dr. J. B. Tatum
jtatum@uvic.ca



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Classical Mechanics (last updated: 2013 September 22)


Chapter 1.    Centres of Mass

1.1Introduction and Some Definitions
1.2Plane Triangular Lamina
1.3Plane Areas
1.4Plane Curves
1.5Summary of the Formulas for Plane Laminas and Curves
1.6The Theorems of Pappus
1.7Uniform Solid Tetrahedron, Pyramid and Cone
1.8Hollow Cone
1.9Hemispheres
1.10Summary


Chapter 2.    Moment of Inertia

2.1Definition of Moment of Inertia
2.2Meaning of Rotational Inertia
2.3Moments of Inertia of Some Simple Shapes
2.4Radius of Gyration
2.5Plane Laminas and Mass Points distributed in a Plane
2.6Three-dimensional Solid Figures. Spheres, Cylinders, Cones.
2.7Three-dimensional Hollow Figures. Spheres, Cylinders, Cones.
2.8Torus
2.9Linear Triatomic Molecule
2.10Pendulums
2.11Plane Laminas. Product Moment. Translation of Axes (Parallel Axes Theorem).
2.12Rotation of Axes
2.13Momental Ellipse
2.14Eigenvectors and Eigenvalues
2.15Solid Body
2.16Rotation of Axes - Three Dimensions
2.17Solid Body Rotation. The Inertia Tensor.
2.18Determination of the Principal Axes
2.19Moment of Inertia with Respect to a Point
2.20Ellipses and Ellipsoids
2.21Tetrahedra


Chapter 3.    Systems of Particles

3.1Introduction
3.2Moment of a Force
3.3Moment of Momentum
3.4Notation
3.5Linear Momentum
3.6Force and Rate of Change of Momentum
3.7Angular Momentum
3.8Torque
3.9Comparison
3.10Kinetic energy
3.11Torque and Rate of Change of Angular Momentum
3.12Torque, Angular Momentum and a Moving Point
3.13The Virial Theorem


Chapter 4.    Rigid Body Rotation

4.1Introduction
4.2Angular Velocity and Eulerian Angles
4.3Kinetic Energy
4.4Lagrange's Equations of Motion
4.5Euler's Equations of Motion
4.6Force-free Motion of a Rigid Asymmetric Top
4.7Nonrigid Rotator
4.8Force-free Motion of a Rigid Symmetric Top
4.9Centrifugal and Coriolis Forces
4.10The Top


Chapter 5.    Collisions

5.1Introduction
5.2Bouncing Balls
5.3Head-on Collision of a Moving Sphere with an Initially Stationary Sphere
5.4Oblique Collisions
5.5Oblique (Glancing) Elastic Collisions, Alternative Treatment


Chapter 6.    Motion in a Resisting Medium

6.1Introduction
6.2Uniformly Accelerated Motion
6.3Motion in which the Resistance is Proportional to the Speed
6.4Motion in which the Resistance is Proportional to the Square of the Speed.


Chapter 7.    Projectiles

7.1No Air Resistance
7.2Air Resistance Proportional to the Speed
7.3Air Resistance Proportional to the Square of the Speed


Chapter 8.    Impulsive Forces

8.1Introduction
8.2Problems


Chapter 9.    Conservative Forces

9.1Introduction
9.2The Time and Energy Equation
9.3Examples
9.4Virtual Work


Chapter 10.    Rocket Motion

10.1Introduction
10.2An Integral
10.3The Rocket Equation
10.4Problems


Chapter 11.    Simple and Damped Oscillatory Motion

11.1Simple Harmonic Motion
11.2Mass Attached to an Elastic Spring
11.3Torsion Pendulum
11.4Ordinary Homogeneous Second-order Differential Equations
11.5Damped Oscillatory Motion
11.6Electrical Analogues


Chapter 12.    Forced Oscillations

12.1More on Differential Equations
12.2Forced Oscillatory Motion
12.3Electrical Analogue


Chapter 13.    Lagrangian Mechanics

13.1Introduction
13.2Generalized Coordinates and Generalized Forces
13.3Holonomic constraints
13.4The Lagrangian Equations of Motion
13.5Acceleration Components
13.6Slithering Soap in Conical Basin
13.7Slithering Soap in Hemispherical Basin
13.8More Examples
13.9Hamilton's Variational Principle


Chapter 14.    Hamiltonian Mechanics

14.1Introduction
14.2A Thermodynamics Analogy
14.3Hamilton's Equations of Motion
14.4Examples
14.5Poisson Brackets


Chapter 15.    Special Relativity

15.1Introduction
15.2The Speed of Light
15.3Preparation
15.4Speed is Relative. The Fundamental Postulate of Special Relativity.
15.5The Lorentz Transformations
15.6But This Defies Common Sense
15.7The Lorentz Transformation as a Rotation
15.8Timelike and Spacelike 4-Vectors
15.9The FitzGerald-Lorentz Contraction
15.10Time Dilation
15.11The Twins Paradox
15.12A, B and C
15.13Simultaneity
15.14Order of Events, Causality and the Transmission of Information
15.15Derivatives
15.16Addition of Velocities
15.17Aberration of Light
15.18Doppler Effect
15.19The Transverse and Oblique Doppler Effects
15.20Acceleration
15.21Mass
15.22Momentum
15.23Some Mathematical Results
15.24Kinetic Energy
15.25Addition of Kinetic Energies
15.26Energy and Mass
15.27Energy and Momentum
15.28Units
15.29Force
15.30Electromagnetism


Chapter 16.    Hydrostatics

16.1Introduction
16.2Density
16.3Pressure
16.4Pressure on a Horizontal Surface. Pressure at Depth z
16.5Pressure on a Vertical Surface
16.6Centre of Pressure
16.7Archimedes' Principle
16.8Some Simple Examples
16.9Floating Bodies


Chapter 17.    Vibrating Systems

17.1Introduction
17.2The Diatomic Molecule
17.3Two Masses, Two Springs and a Brick Wall
17.4Double Torsion Pendulum
17.5Double Pendulum
17.6Linear Triatomic Molecule
17.7Two Masses, Three Springs, Two brick Walls
17.8Transverse Oscillations of Masses on a Taut String
17.9Vibrating String
17.10Water
17.11A General Vibrating System
17.12A Driven System
17.13A Damped Driven System


Chapter 18.    The Catenary

18.1Introduction
18.2The Intrinsic Equation to the Catenary
18.3Equation of the Catenary in Rectangular Coordinates, and Other Simple Relations
18.4Area of a Catenoid


Chapter 19.    The Cycloid

19.1Introduction
19.2Tangent to the Cycloid
19.3The Intrinsic Equation to the Cycloid
19.4Variations
19.5Motion on a Cycloid, Cusps Up
19.6Motion on a Cycloid, Cusps Down
19.7The Brachystochrone Property of the Cycloid
19.8Contracted and Extended Cycloids
19.9The Cycloidal Pendulum
19.10Examples of Cycloidal Motion in Physics


Chapter 20.    Miscellanea

20.1Introduction
20.2Surface Tension
20.2.1Excess Pressure Inside Drops and Bubbles
20.2.2Angle of Contact
20.2.3Capillary Rise
20.3Shear Modulus and Torsion Constant
20.4Viscosity
20.4.1Poiseuille's Law
20.4.2The Couette Viscometer


Appendix A.    Miscellaneous Problems

Appendix B.    Solutions to Miscellaneous Problems




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