PH3111 Theoretical Mechanics II ..... (3-0-0) s ..... 3 Cr

Prerequisite: PH3110.

Text (Spring 2006):

• Analytical Mechanics, 7 ^th Ed, Fowles & Cassiday (ISBN 0-534-49492-7)

• Analytical Mechanics, 6 ^th Ed, Fowles & Cassiday (ISBN 30223172)

Analytical Mechanics, 5^th Edition, Fowles and Cassiday
Classical Dynamics of Particles and Systems, 3^rd edition, Marion and Thornton

Topics (# of Lectures)

Newtonian Mechanics of Systems of Particles (8)

• Dynamical Systems
• Center of Mass and Linear Momentum
• Angular Momentum and Kinetic Energy of a System
• The Two-Body Problem
• Direct Impact of Two Particles
• Oblique Impact of Two Particles
• Motion of a Body with Variable Mass

Mechanics of Rigid Bodies - Planar Motion (5)

• Center of Mass of a Rigid Body
• Statics of a Rigid Body
• Rotation about a Fixed Axis - Moment of Inertia
• The Physical Pendulum
• Laminar Motion of a Rigid Body

Mechanics of Rigid Bodies - Motion in Three Dimensions (8)

• The Inertia Tensor
• Rotational Kinetic Energy
• Principal Axes of a Rigid Body
• Euler's Equations of Motion of a Rigid Body
• Free Rotation of a Rigid Body
• Motion of a Symmetrical Top with One Point Fixed - Precession and Nutation

Hamilton's Principle and the Calculus of Variations (3)

• A Brief History of Variational Principles
• Hamilton's Principle
• Derivation of the Euler-Lagrange Equation

Lagrangian and Hamiltonian Mechanics (8)

• Constraints and Generalized Coordinates
• Lagrange's Equations of Motion
• Generalized Momenta and Ignorable Coordinates
• Conservation of Energy
• Conservation Laws and Symmetries
• The Hamiltonian and Hamilton's Equations

Oscillating Systems (5)

• Two Coupled Harmonic Oscillators
• Weak Coupling
• Normal Coordinates and Normal Modes
• Transition for a Discrete to a Continuous System

Vibrating Strings (4)

• Transverse Motion of a Stretched String
• D'Alembert's Solution of the Wave Equation
• Normal Modes of a Stretched String

Course Rationale: The second course at the intermediate level in mechanics, one of the well-established core areas of Physics. It provides an in-depth study of mechanics at a higher level of mathematical skill than in the introductory course and covers material considered essential for an undergraduate physics major and very useful for closely related majors. It is a required course for all SPH and an elective for SAP majors.