This course deal with the Newtonian, Lagrangian and Hamiltonian formulations of classical mechanics.
Resources
Table of Contents
The main book used in this course is
Classical Mechanics, by John R. Taylor, University Science Books (2005)
ISBN 189138922X
Another excellent resource is the book Classical Dynamics by David Tong, Professor at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK. (Professor Tong made these lectures available to the public via the website linked above. The author’s copyright stipulates: “Lecture notes copyright © 2004 David Tong unless otherwise credited. Permission is granted to copy and distribute freely, so long as proper attribution is given, no alterations are made, and no monetary profit is gained.”)
Students should also visit and explore Professor Tong’s Lectures on Classical Dynamics website.
Class notes
Here you can find links to some of the lecture notes used in class. The notes primarily cover material in the way in which it is discussed in the textbook. The links and the notes are added, edited, and updated during the semester. (The class notes are written and edited by Andrea Ferroglia.)
Newtonian mechanics

 Space, time, mass, force
 Newton’s first and second law of motion
 Momentum conservation
 Newton’s second law in Cartesian coordinates
 Newton’s second law in polar coordinates
 Marble in a half pipe
 Air resistance
 Air resistance linear in the velocity
 Projectile range for linear air resistance
 Air resistance quadratic in the velocity
 Horizontal motion with quadratic air drag
 Free fall with quadratic air drag
 Motion of a charged particle in a magnetic field
 Collisions
 Rockets
 Center of mass
 Angular momentum of a particle
 Conservation of angular momentum
 Workenergy theorem
 Potential energy
 Force as gradient of a potential
 Curl of a conservative force
 Linear one dimensional systems
 Curvilinear one dimensional systems
 Harmonic oscillator
 Simple harmonic motion
 Damped oscillator
 Drivendamped oscillator
Lagrangian mechanics

 Calculus of variations
 EulerLagrange equation
 The brachistochrone problem
 Euler Lagrange equations for multivariate problems
 Configuration space
 Lagrangian
 Lagrangian for one particle moving on a flat surface
 Gradient in polar coordinates
 Lagrangian for N unconstrained particles
 Simple pendulum
 Constrained systems
 Lagrange equations in holonomic systems
 Atwood machine
 Particle moving on the surface of a cylinder
 Block on a sliding wedge
 Bead on a hoop
 Ignorable coordinates and conservation laws
 Nonuniqueness of the Lagrangian
 Charged particle in a magnetic field
 Lagrange multipliers
 Atwood machine with Lagrange multiplies
 Two body problem
 Center of mass frame
 Effective potential
 Orbit equation
 Orbital period
 Relation energyeccentricity
 Unbounded orbits
Hamiltonian mechanics

 Hamiltonian
 Hamilton’s equations in one dimension
 Bead on a straight wire
 Hamilton’s equations for the Atwood machine
 Hamilton’s equations in many dimensions
 Central force
 Particle on a cone
 Ignorable coordinates
 Phase space
 Harmonic oscillator phase space
 Falling mass phase space
 Liouville’s theorem
Mechanics of the Rigid Bodies

 Properties of the center of mass
 Rotations about a fixed axis
 Simple products of inertia
 Rotations about an arbitrary axis
 Inertia tensor for a solid cube
 Inertia tensor for a solid cone
 Principal axes
 Rotational kinetic energy
 Eigenvalue equation
 Principal axes of a cube
 Weak torque
 Euler equations
 Euler equations with zero torque
 Euler angles
 Spinning Top