Mechanics II syllabus

Mechanics II: Syllabus

I. Calculus of variations (Chapter 6): review

Formal methods for finding stationary values of integral quantities (minimum distance between two points, minimum time to rescue drowning swimmer, minimum surface area for a soap bubble on a frame….)

II. Hamilton’s Principle: Lagrangian and Hamiltonian dynamics (Chapter 7)

Application of the calculus of variations to reformulate mechanics in terms of the minimization of the Lagrangian (sometimes called the least action principle). Advantages to this approach. Beyond classical mechanics.

III. Central force motion (Chapter 8)

Motion (orbits, etc.) of two bodies with a force directed along the line connecting their centers. Using conservation theorems, the center of mass frame of reference, and effective potential energies.

Exam I (20% of grade)

IV. Dynamics of a system of particles: Two particle collisions (Chapter 9)

What you can do with conservation laws, continued.

V. Motion in a non-inertial reference frame (Chapter 10)

So far, we have usually assumed an inertial reference frame. How to do physics if you’re not in one (on the rotating, orbiting earth for example.) This may convince you to always do physics in inertial reference frames. Can you?

Exam II (20% of grade)

VI. Rigid Body Motion (Chapter 11)

How to do physics if you’re not working with point particles. You should bring to class appropriate rigid objects (tennis rackets, tops, boomerangs...) to discuss.

VII Coupled Oscillations (Chapter 12)

Normal modes of coupled systems. Connections to molecular vibrations and to waves in solids.

VIII Selected topics as time permits

Final Exam (Comprehensive, 20% of grade)

The exact date of the exams will be announced at least one week in advance. The final exam will be at the assigned time during finals week. It will be comprehensive. Homework will be assigned every class and will count 25% of the grade.

In accordance with University policy, if you have a documented disability and require accommodations to obtain equal access in this course, please contact the instructor at the beginning of the semester or when given an assignment for which an accommodation is required. Students with disabilities must verify their eligibility through the Office of Student Disability Services (SDS) in the Michael Schwartz Student Services Center (672-3391).