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PHYS326

PHYS326 (Classical Mechanics II) is a 3-credit hour course that counts as a technical elective for both EEs and CEs. It is offered in the fall and spring semesters.

Content Covered

  • Simple harmonic oscillators
  • Multiple degree of freedom oscillations
  • Symmetries
  • Nonlinear dynamics and chaos
  • Rigid body mechanics
  • Hamiltonian mechanics
  • Continuum mechanics

PHYS326 is a continuation of PHYS325, covering more topics in classical mechanics and going into greater detail than its prerequisite. PHYS326 begins with a review of the simple harmonic oscillator from PHYS325. Much of the first half of the course is spent on analyzing multiple degree of freedom, linear, coupled oscillators, which heavily involves linear algebra. In this part of the course, students learn to find the natural frequencies and mode shapes of systems of coupled oscillators to determine equations of motion. The course then covers symmetries and coordinate transformations, as well as forced motion of multiple degree of freedom systems and Green's matrices. The next section of the course involves nonlinear dynamics and chaos. In this section, Lyapunov exponents, bifurcation diagrams, fractals, phase portraits, and Poincare sections are covered. Numerical solution of differential equations using Euler's method and the Runge-Kutta method is also covered.

The mechanics of rigid bodies, objects with continuous mass distributions, as opposed to point masses, and no deformation, is then covered. In this section, the inertia tensor, parallel axis theorem, Euler equations, rotation and orientation matrices, and Euler angles are introduced. The dynamics of axially symmetric bodies (tops) are analyzed in more detail. Hamiltonian mechanics is then reintroduced in greater detail than in PHYS325, including Hamilton's equations of motion, Poisson brackets, and Liouville's theorem. The course then moves to continuum mechanics. As opposed to rigid body mechanics, which covers objects without spatial deformation, continuum mechanics covers objects whose relative positions can change with time. Within continuum mechanics, the course first analyzes the case of waves on a string, first with and then without forcing. 2D and 3D waves are then covered, with applications to acoustics. Continuum mechanics are then covered more rigorously; the concepts of stress and strain are introduced and Hooke's law is derived. The course concludes with an introduction to fluid mechanics, covering the continuity equation, Bernoulli's theorem, and the Navier-Stokes equations.

Prerequisites

PHYS325 is the only official prerequisite to PHYS326, as the course is a continuation of PHYS325. It is also a good idea to have a background in linear algebra from MATH257 for this course, as linear algebra is used heavily throughout PHYS326.

When to Take It

Take this course if you are interested in classical mechanics. It is best to take this course directly after taking PHYS325.

Course Structure

PHYS326 has two lectures per week, where course content is introduced. In addition to the lecture, PHYS326 also has a weekly discussion section. Attendance in discussion is also required, though students do not need to submit any work. During discussion, students work through provided discussion problems, which can occasionally be ahead of lecture. To be prepared for the homework and exams, it is important to work through these problems and ask the TA questions.

Homework is assigned weekly, covering the concepts introduced in lecture the prior week. The homework is around the same difficulty as that of PHYS325. Expect to spend around 6 hours on the homework. Extra credit is provided on the homeworks for students who typeset their homeworks using LaTeX.

Finally, PHYS326 has two in-class midterm exams and one final exam. The exams can be difficult and often involve proofs of concepts derived in lecture. It is recommended to go through their homework and discussion problems in preparation for the exams, as past exams are not provided. It is also a good idea to go through each of the proofs done in lecture, as they can reappear on the exam. Students are allowed to write their own formula sheet.

Instructors

Recently, Professor Golding has taught this course.

Course Tips

Working through the discussion and homework problems diligently and working to understand how concepts are derived will allow any student to do well in this course.

Life After

While no courses in classical mechanics directly follow this one, physics students who have taken this course will be better prepared for courses like PHYS427 - Thermal and Statistical Physics and PHYS486 - Quantum Physics I.

Infamous Topics

  • Rigid body motion: Calculations can be tedious.

Resources

The optional textbook, Classical Mechanics, by John Taylor, is a good resource. The instructor provides relevant sections for students to read in addition to the prelectures for greater understanding of the material. Professor Adshead's lecture notes are also a good resource.