Course Information

Physics 312 -- Classical Dynamics -- Winter 2021

      The science of dynamics is one of the greatest triumphs of human thought.  Centered around the question "How can motion be described and predicted?", dynamics, or analytical mechanics, is the most fundamental field of science, asking the most basic questions.  The answers to these questions involve subtle ideas and the use of advanced mathematics, and seem to provide insight into the very framework of the physical laws of the universe.
     Mechanics began with the investigations of Galileo and Newton in the early 1700s.  Appropriately, we will begin with a review of Newton's laws of motion, taking a more sophisticated point of view than we have previously.  After developing a language for expressing motion, involving vectors, coordinate systems, transformations, and differential equations, we consider Newton's laws for the motion of point particles.  We will take advantage of the familiar nature of this material to introduce an important theme of the course--numerical solution of mathematically intractable problems.  We will learn how to analyze mechanical systems numerically on the computer, using Mathematica.  Numerical solution of problems is an important part of doing physics, not just because many realistic problems cannot be solved analytically, but also because a new tool in our mathematical repertoire can often provide new insights into problems even when they are approachable by other methods.  We will consider the mechanics of systems of particles, developing the important conservation theorems of energy, momentum, and angular momentum.  We will then learn about a powerful and very convenient method of approaching mechanics problems – Lagrangian mechanics.  As an in-depth example of the motion of a system of particles, we will study planetary motion, or the two-body problem.  As an extended investigation of the mechanics of systems, we consider the important and fascinating subject of rigid body motion, after first generalizing Newton's laws to describe motion in rotating (or otherwise accelerating) coordinate frames.  Our study of rigid body motion is in a sense the high point of the course, tying together many of the ideas we have developed for describing the motion of systems of particles.
     Our study of mechanics will be for many of you your first course in "intermediate-level physics.”  Intermediate-level physics, as I define it at least, involves learning to use some advanced mathematical techniques from differential equations, linear algebra, or vector calculus, as well as a more sophisticated discussion of theory and an increased emphasis on derivation of results.  The transition from introductory-level to intermediate-level physics is not an easy one, although the increased confidence and deeper understanding one gains from intermediate-level physics makes the effort very worthwhile.  You may find this course and the textbook rather challenging compared to your previous physics courses--this is intentional, and I think the effort you put in will pay off in increased insight and satisfaction.  The intermediate-level physics courses (Mechanics, Electricity & Magnetism, Quantum Mechanics, Optics, and Statistical Mechanics) comprise the heart of the physics major.

Homework and computer projects	25%
Math review	5%
In-class exams	20% each
Final exam (cumulative)	30%