ANALYTICAL MECHANICS (PHY 340.001)-Fall Semester, 2004

Text:

Analytical Mechanics, 7th Ed., by Fowles and Cassiday, Saunders College Publishing (ISBN 0-534-40813-3)

Meets at:

9:00-9:50 MWF, Willet Science Center (WSC) Room 106

Prerequisites:

MATH 293 and 330, PHY 162

Instructor:

Dr. Randall D. Peters

Office:

WSC Room 115, Office phone: 301-2747

Office hours:

MWF 8:30-9:00, 2:00-2:30, TR 8:30-9:30, or by appointment.  

e-mail:

peters_rd@mercer.edu

personal homepage:

http://physics.mercer.edu/petepag/nonlin.htm

physics department homepage:

http://physics.mercer.edu

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This course is concerned with Newton's laws and also techniques to solve problems using energy, rather than force considerations. Primary attention will be given to systems in which the state variables evolve in time, particularly periodic variation. The classic examples of such are various mechanical oscillators, and also the gravitational two-body problem. These systems will be treated primarily by analytic means, although some features, such as power spectra, will be determined with the computer. Other systems of nonlinear type will also be treated numerically, using Quickbasic. An introduction will be provided to the new science of chaos.

                     Expectations
Incoming-Students should already have mastered essential elements of:
(i) foundation mathematics
(ii) graphical representation of results, whether experimental data or theoretical calculations, and
(iii) standard convention in the representation of scientific results.
Outgoing-By the end of this course, the student should be able to:
(i) demonstrate improvements in scientific communication, both
verbal and written, through self-consistent integration of mathematical
formulae and the English language,
(ii) better understand, both conceptually and quantitatively, some of the classic systems of physics,
(iii) appreciate limitations that derive from approximations frequently used, but which can prove unacceptable,
(iv) address a new and important branch of science, that of ``Chaos''.

Ch. 1, Quick review of:
(a) units standardization and vector math,
(b) kinematics to include spherical and cylindrical coordinates.
Ch. 2, Newtonian Mechanics:
(a) Position dependent forces and potential energy,
(b) Velocity dependent forces,
(c) Euler-Cromer numerical integration^* using Quickbasic.
Ch.3, Oscillatory mechanical systems:
(a) Simple harmonic oscillator (SHO), no drive, no damping,
(b) SHO with idealized (rarely adequate) damping,
(c) Phase space concepts,
(d) Driven SHO with damping,
(e) Nonlinear oscillator (Duffing^*), to introduce chaos.
Ch. 10, ``Quick and dirty'' treatment of Lagrangian and Hamiltonian mechanics:
(a) Generalized coordinates,
(b) Recipe for the Lagrangian from Kinetic and Potential energy functions,
(c) Hamilton's canonical equations.
Various types of PENDULUM <sup>*</sup>: Examples of the use of Hamilton's technique to obtain equations of motion that are ideally configured for numerical treatment.
Ch. 4, 3-D particle Motion:
(a) Projectile,
(b) Lorentz force (E-M) problems.
Ch. 5, Non-inertial (accelerated) Reference Frames:
(a) Static cases,
(b) Dynamic-(i) Coriolis, and (ii) Centrifugal forces,
Ch. 6, Two-body Problem:
(a) Kepler's Laws and his equation,
(b) Poincare's three-body problem.
Ch. 7, Systems of Particles (a) Effective potential and Lagrangian points of the solar system,
(b) Center of mass system, collisions,
(c) Rocket problem,
(d) ``Sling-shot''(Gravity assist) mechanics,.
Ch. 8,9; Rigid body mechanics:
(a) Rotation coordinate transformations,
(b) Parallel axis theorem and Moment of inertia tensor,
(c) Eigenvalue problem involving principal axes,
(d) Euler's equation,
(e) the Gyroscope,
(f) Tidal Force^*.
Ch. 11, Normal coordinates, coupled harmonic oscillators.

^* Material not treated (or partially treated) in the text. Handouts will be provided in some cases.

Final Exam: Thurs, 9 Dec., 9 a.m.-noon.

Grading Scale: 60-D-70-C-80-B-90-A-100
(based on: Homework-1/3, Midterm-1/3 (week of 4 October--W or F), and Final-1/3.

• I don't have a formal attendance policy-be forewarned, however, that students with more than an occasional absence usually do poorly.
• Quizzes and exams may be made-up if the student has an official excuse. There is no extra-credit work.
• The College of Liberal Arts academic misconduct policy will be followed.
• Any student who receives failing grades during the course is urged to meet with the instructor and discuss such work.
• If you have a problem of any kind, my door is open to you. (If your schedule should be in conflict with my office hours, then attempt to arrange an appointment either: (i) during class, or (ii) by a chance meeting using the information posted on my door.)
• Out of courtesy for all those participating in the learning experience, all cell phones and pagers must be turned off before entering any classroom, lab, or formal academic or performance event .
• Students who believe that they possess disabilities for which accommodation is required must so inform the instructor at the close of their first class meeting. They must then indicate the nature of their disability and the sort of reasonable accommodation requested. If you believe that you possess a disability for which reasonable accommodation must be made, you must consult with the instructor of this class immediately after your first class meeting. You will then identify the disability, and the reasonable accommodation requested. The instructor will refer you to the office of the Dean of Students for evaluation, documentation of your disability, and a recommendation as to the accommodation, if any, to be provided.  If you do NOT consult with the instructor and follow up at the office of the Dean of Students, as provided above, you will thereby waive any claim to a disability and the right to any accommodation pertaining thereto.