2.032 Course Syllabus

Review

inertial frames; linear momentum; force; Newton's second law; work and energy; moment of force; angular momentum; moving frames; centrifugal and Coriolis forces.

Lagrangian and Hamiltonian Mechanics

generalized coordinates; holonomic and non-holonomic constraints; Virtual work; Hamilton's principle of least action; Lagrange's equations; symmetry and conservation laws; similitude and dimensional analysis; Legendre transforms; Hamilton's equations; canonical transformations; action-angle variables.

Dynamics of Discrete Systems

Oscillations and vibrations; linearity and superposition; normal modes; free and forced motion; resonance; parametric excitation; damping; maps and flows; phase plane analysis; stability, instability and bifurcation; chaos.

Motion of Rigid Bodies

kinematics; Euler angles; inertia tensor; angular velocity and angular momentum; equations of motion; Poinsot's description; soluble problems; tops and gyroscopes.

Calculus of Variations

Euler-Lagrange equations; constraints and Lagrange multipliers; Fermat's principle; optimal control.

Dynamics of Continuous Systems

Hamilton's principle again; waves vs. vibrations; strings and chains; examples from elasticity, fluid mechanics, optics and acoustics.