Spring 2015 Syllabus for PH303 (Theoretical Mechanics)

Scott Heinekamp (scotth@wells.edu) Straton 302 ext 3361 (http://henry.wells.edu/~scotth)
Office Hours Tues 9:30-11:00 & Wed 11:30-12:30 or by appt
Course Goals
-- to build on the knowledge gained in Fundamentals of Physics I and II, as well as introductory mathematics courses;
-- by way of the damped harmonic oscillator as a paradigmatic example, to learn about the ways one frames a physical problem as a differential equation, and then to explore various methods of solving such a thing, either exactly or in some approximate way;
-- from such solutions, to relate the mathematical results to the implications for the physics;
-- as a second paradigmatic example, to learn about the central force problem in three dimensions, and the manifold insights it can give to the methodolodies that classical mechanics entails;
-- to explore other important topic areas in intermediate mechanics, including systems of particles and the motions associated with them, and how one treats motion that occurs in non-inertial (accelerating) frames of reference;
-- to introduce an alternative and more abstract way of thinking about mechanics: the Lagrangian method
-- at all times, to be willing to develop analytical techniques to suit the issues at hand, no matter how abstract the methods need to be

Course Description
Theoretical Mechanics is an in-depth study of the description and explanation of translational and rotational motion. The subject matter forms the core of classical physics: it is as much about methodology as about the topics themselves. Because the class is small, I hope to discuss topics that are of interest to the class, since we can't hope to legitimately cover the whole field. Generally, though, we will revisit Newtonian dynamics as a review; look in depth at oscillations; delve into the phase plane method ; discuss in depth central-force motion and the consequences of angular momentum conservation; see how things are described in an accelerating (particularly, rotating) frame of reference; and learn about (and use) the Lagrangian method.

Textbook and reserve materials
Text is Classical Mechanics by Douglas Gregory.
Useful to consult: Classical Mechanics (5th Edition) by Kibble and Berkshire; Classical Dynamics of Particles and Systems (2nd ed.) by Marion; Classical Mechanics: A Modern Perspective (2nd ed.) by Barger and Olsson. In a field such as this, even 'old' books are excellent, so I encourage you to paw through the library's collection.

The set of homework assignments may be found at Homework Assignment, where the annotated homework sets will appear. This will be updated regularly. Most but not all problems will be taken from the text.

Grading System
Homework and Class Participation (40% total). Attendance is expected at every class. There is no need for any electronic devices to be used during this class. Violations of these policies will be noted and will negatively impact your score in this area.
Exams: 3 of them 20% each (60% total). The third exam will be at the time of the final exam.

Lecture Schedule
Week 1: Week of 19 Jan Review of Mathematics (Ch 1, ch 18.1-3) Vectors. Derivatives. Taylor's theorem. Scalars, vectors...
Week 2: Week of 26 Jan (Ch 2.1-2.6) Kinematics Position, velocity and acceleration in 1d. Circular motion, in cartesian and in polar coordinates. Elementary rotational motions. Relative motion and frames of reference.
Week 3: Week of 2 Feb Elementary Dynamics (Ch 3.1-5, 4.1-5) Newton's laws: forces. Multiple interactions. Center of mass. Elementary Examples: Free-Fall; One-d Gravity; Damped motion. Circular motion in gravity.
Week 4: Week of 9 Feb Exam 1 & Harmonic Motion (Ch 5.1-3) Continuation and review. Exam 1. The undriven damped harmonic oscillator.
Week 5: Week of 16 Feb Driven Oscillations & An Alternative Approach Ch 5.4, 8.2-3) The driven oscillator. Resonance. The Q-factor. The Phase Plane.
Week 6: Week of 23 Feb Energetics (Ch 6.1-5) Definitions. Obtaining kinematics from energy conservation. Small oscillations near a potential energy minimum.
Week 7: Week of 2 Mar Orbits in Attractive Forces (Ch 7.1-4) The effective one-body problem. The effective one-d orbit problem. Circular orbits and small deviations.
Week 8: Week of 16 Mar Kepler's Laws (Handout on conic sections; Ch 7.5) Orbits in Newtonian gravity. Conic sections for their own sake. Kepler's Laws.
Week 9: Week of 23 Mar Exam 2 & Systems (Class notes, Ch 9.3) System quantities. Energy conservation for conservative systems: falling chains
Week 10: Week of 30 Mar More About Systems (Ch 9.4, Ch 10.1-5,8) Rigid body rotations about a 'simple' axis. The moment of inertia. System momentum and its conservation. Rocket motion. The two-body problem revisited.
Week 11: Week of 6 Apr Angular Momentum (Ch 11.1-6) Moments of the force and of the momentum. Rigid body angular momentum. Conservation of angular momentum. Planar motion.
Week 12: Week of 13 Apr Accelerating Frames (Ch 17.1-3) Ficticious forces, especially in rotating coordinate systems.
Week 13: Week of 20 Apr Lagrangian Mechanics (Ch 12.1-12.7) Constraints and virtual work. dAlembert's principle. Lagrange's equations. Use of the Lagrangian.
Week 14: Week of 27 Apr Examples & review for Exam 3/Final Exam

Final exam -- TBA during finals week