Lectures: 1-2pm on Mon, Wed and Fri, in Hennings 202.

Calendar Description: Newtonian mechanics, non-inertial frames, central potentials, Kepler's laws, variational calculus, Lagrangian dynamics, rigid body motion, Hamiltonian mechanics, Poisson brackets, canonical, Hamilton-Jacobi theory, action angle variables.

Credits: 3

Prerequisites: One of MATH 200, MATH 217, MATH 226 and one of MATH 221, MATH 223, MATH 152 and either (a) SCIE 001 or (b) one of PHYS 12, PHYS 107, PHYS 157, PHYS 170, PHYS 216 and one of PHYS 102, PHYS 108, PHYS 158.

Corequisites: MATH 215.

Grading: (tentatively)

• 50%: assignments
• 50%: final exam

Exam Topics

EXTENDED DESCRIPTION: This course is intended to give an understanding of classical Newtonian mechanics using the Lagrangian and Hamiltonian formulations. When Newton created classical mechanics in his famous "Principia" in 1687, he wrote everything in terms of local forces acting on bodies; in the case of gravitation this force acted "at a distance" through the empty medium of space. Later on Lagrange and Hamilton gave different formulations, in which forces took a back seat -- everything was derived from a "variational principle", in which massive bodies followed paths for which a quantity S (which we now call the "action") was minimized.

The course will begin by looking at Lagrangian mechanics -- Lagrange's equations will be derived using the "principle of least action", and we will then see how these equations allow us to solve practical problems in a very streamlined way (which is often much simpler than applying Newton's laws to these problems). We will focus particularly on the motion of bodies in central force fields, on rigid body motion, and on the dynamics of oscillators. Time permitting, we will also develop the Hamiltonian framework, in which particles move in "phase space", and momentum P and position Q are treated as independent variables, leading to the Hamilton-Jacobi equation and action-angle variables.

The main goals of the course will be (i) to give you a deeper understanding of what classical mechanics is (and help you understand variational methods while doing this); and (ii) to teach you to use the powerful tools of Lagrangian and Hamiltonian mechanics to solve practical problems in classical mechanics.

Tentative Syllabus: