Department of Physics

Wake Forest University

Department of Physics

Wake Forest University

Analytical Mechanics

e-Syllabus

Instructor: Dr. David Carroll

Class Location: 103 Olin Hall

Time: 12:30 - 1:45 T/TH

Ave. Out of Class Prep Time: 2 hours/class

Mathematical expressions for the motion of solid objects in space and time, can be formulated using a number of fundamental principles. "Newtons Laws" are the best known and simplest of these. They make direct reference to an applied force vector which results in the vector quantities of displacement, velocity and acceleration. With this we may accurately predict in time, the motion of objects given that the applied forces and initial conditions are well defined and well behaved. However, there are other basic and universal principles upon which a formal expression of motion might be derived. These are principles of conservation, minimization, and symmetry. They are based on the formal parameterization of time evolution in dynamical systems. Analytical Mechanics / Dynamics seeks to formulate the prediction of motion using such principles, thereby extending the range of problems accessible to mathematical understanding.

Why does the physicist need Analytical Mechanics / Dynamics? All areas of modern physics research are touch by it. It forms the basis of quantum mechanics formulations. It provides the underpinnings of many astrophysical models, is used in the description of chaos, and forms a bridge to statistical mechanics through classical ensemble theory. It gives us a more complete vision of how the symmetries of space and time are connected to the motion of objects.

Welcome to PHYS 337/637

This course will provide a mathematical introduction of to variational methods of mechanics (Lagrangian and Hamiltonian formulations) and the geometries of global behaviors. The course is highly theoretical developing an advanced formalism for dynamics. The 639 section will be assigned extra reading and homework and is an excellent refresher for those preparing for the graduate qualifier. This course runs 1/2 a semester and is evaluated midterm (October).

Topics

I. Variational Calculus

Variational calculus,

Introduction to Virtual work,

Maupertuis' principle and the action functional,

Homework assignment 1.

II. The Lagrangian

Generalized coordinates, constraints and minimum coordinate sets.

Derivation of the Lagrangian

The resulting equations of motion.

Homework assignment 2.

Exam 1

III. The Hamiltonian

Derivation of Hamilton's equations

Conservation principles

Phase Space

Homework assignment 3.

Exam 2

Grading policy

There are three HW assignments and two exams in this class. Each part will present a specific number of points that you can earn toward a total of 100 points. Roughly the breakdown will be 10 points on each of the HW assignments and 35 points on the Exams. Grades are assigned based on the total number of points accumulated by the end of the class. Each student is expected to schedule at least one meeting with me to discuss your progress in the class and your grading. This should take place well before the end of the class.

Attendance and Examination Policy

Attendance is required for the class. It is important to realize that not all topics covered will be found in the text. Students must work independently on all assignments; including hw and exams.

Text

Author: Grant R. Fowles & George L. Cassiday

Edition: 7th Edition 2004

Office Hours

Tuesday and Thursday, 10:00 - 11:00 (am) or by appointment

214 Olin Physical Laboratory

Reynolda Campus

Wake Forest University

Winston-Salem NC 27109

ph: 336 727 1806

email: carroldl@wfu.edu