Course Information

Course Description

This is a one-semester course on Classical Mechanics, aimed at undergraduate (PHY422) and first-year graduate students.

The course will cover the following topics:

  1. Lagrangian Mechanics
    • constrained motion
    • D’Alembert’s principle
    • Principle of Least Action
    • Euler-Lagrange equations of the first and second kind
    • Noether’s theorem and symmetries
  2. The Kepler Problem
    • orbits and stability, Bertrand’s theorem
    • conserved quantities
    • perihelion precession
    • scattering
    • Lagrange points
  3. The Rigid Body
    • rotating coordinate systems
    • Euler angles
    • inertia tensors and principal axes
    • Euler equations
    • free rigid body
    • wobbling motion
  4. Normal Modes
    • coupled oscillators
    • generalized eigenvalue problems
    • normal modes
    • normal coordinates
  5. Hamiltonian Mechanics
    • Hamiltonian equations of motion
    • phase space
    • canonical transformations
    • Poisson brackets

Depending on our progress, we will discuss some of the following topics:

  • Nonlinear Dynamics
    • anharmonic oscillators
    • perturbative treatment; Lindstedt-PoincarĂ© method
    • numerical solution
    • examples of chaotic behavior
  • Classical Field Theory
    • elements of special relativity: Lorentz transformations, Lorentz tensors
    • Lagrangians in field theory
    • equations of motion
    • spontaneous symmetry breaking
  • Perturbation Theory
  • Fluid Dynamics

Course Format

Meetings will be held in person, with an option to join remotely if necessary. Please contact me ahead of time if you intend to join by Zoom (see link in sidebar), if at all possible.

Please note that due to the COVID-19 pandemic, MSU mandates that masks must be worn inside MSU buildings at all times.

The course has a flipped-classroom format: Students are expected to read assigned materials ahead of the class meetings. During the meetings, we will discuss open issues from the readings, and work through exercises in small groups. (For remote attendants, we will employ Zoom’s breakout room functionality if necessary.)

Recommended Textbooks & Materials

There are several textbook options that cover the essential material of the course, but the lectures themselves will not follow one specific text. Topics for each week will be given in some detail on the schedule page, alongside reading assignments that refer to the the following texts:

Analytical Mechanics by Nivaldo Lemos (Cambride University Press, 2018).

Classical Mechanics (3rd Edition) by Herbert Goldstein and Charles P. Poole & John Safko.

Required Technologies

The required technologies and platforms for this course are

  • Zoom for participating remotely in class meetings and office hours,
  • Git for submitting computational projects and accessing certain course materials that will not be posted to the course website (see below),
  • a Python distribution encompassing the Jupyter notebook tools and common scientific libraries (see the computation section),
  • Gradescope for submitting homework, and a means to scan written homework to a PDF file,
  • and your MSU D2L account for checking grades.

Slack

I recommend Slack for collaborative work and discussions outside of the class meetings. An official, members-only Slack channel has been set up.

Code Repository

Course materials will be hosted in a GitLab repository on MSU’s GitLab server. Lecture notes, worksheets, homework assignments, and practice materials will be posted on this website, solutions will only be made available through the repository. The most convenient way to obtain the most up to date version of all materials is to perform a git pull. For more information, check the page’s computation section.

Learning Continuity

A student who cannot attend the course for an extended period should inform me as soon as possible to discuss options for proceeding. These may range from making up for missed work in the same semester, or deferring the grade until completion of work at some agreed-upon later time. See MSU’s policies for deferred grades and medical leave.

Course Continuity

I am working with the Department of Physics & Astronomy to set up contingencies for the event that I should be unable to continue serving as the primary instructor, due to COVID-19 or for any other reason.