Classical Mechanics

Introduction

Classical theoretical physics really began with the work of Sir Isaac Newton (grew up 15 miles from where my mother lived in England). His Principia Mathematica, written to answer a question from Robert Hooke, set out to explain how planets move in elliptical orbits and in the process formulated the basic laws of motion and developed the whole mechanism of calculus to solve problems in this new discipline. More than 300 years later Newton's laws and the calculus remain an excellent description of how the world works (so long as we limit ourselves to speeds that are much slower than light, to objects that are not too small, and to regions of space that are only slightly bent by gravity). You already know Newton's laws and the calculus and have used them to solve a wide range of the simpler problems in mechanics. This course aims to explore some more complex systems. After a few weeks of review we shall go on to develop a reformulation of Newton's mechanics using methods introduced by Euler and Lagrange and refined by Hamilton (William Rowan, not Alexander), methods that Shroedinger adapted to create quantum mechanics.

Course Details

The text for the course is Intermediate Dynamics, by Patrick Hamill.

The course meets three times per week for 75 mins. The first two meetings will normally be traditional lecture time with the usual mixture of my presenting material, doing problems, getting you to answer questions, etc. The Friday meeting will sometimes be the same sort of thing but may also be used for other activities which may include mini-labs, computer work (with Maple), problem solving sessions, and seminars. These will be sessions where individual students present prepared solutions or new material in an environment that should foster questions and class interactions. Following advice from Seth, there will be NO PowerPoint presentations allowed here! At the end of this page I have included some tips from Seth on preparing for seminars.

There will be about 10 weekly homeworks. These will range from moderate drill problems to some really tough problems that should challenge all of you. As usual, reasonable collaboration is encouraged in tackling these problems but the solutions that you hand in must be individual and should indicate which parts of the work were collaborative and which parts your own.

Grading

There will be weekly homework assignments in all weeks that do not also include an exam. Homeworks are due at the start of class on every Friday when there is not an exam.

There will be three take-home exams, one about 1/3 of the way through the course, one about 2/3, and the last in exam week. The final will be due by the end of the registrar's scheduled exam time for this course. There will also be a grade based on your performance in the presentations on the seminar parts of class or other similar activities such as posters. That grade will reflect the clarity, completeness, and depth of your presentations. The complete course grade will be divided between all the activities according to the following formula

		Running Total
Homeworks	50%	50%
Presentations	5%	55%
Midterms (2 @ 15%)	30%	85%
Final Exam	15%	100%

Seth's Tips for Seminars.

1. Nothing will help you better than to start preparing for seminar early. As good as they are, these chapters are not short stories; it would be unpleasant to read the entire chapter in one sitting. Further, read with a scratch pad and writing utensil; work through the presentation of the text. Allow plenty of time. Slogan: "Start early. Work slowly and carefully."
2. Physics is not learned only by reading. To learn the subject one must try out the stuff by talking and writing about it and working through problems. For many of us this process has two purposes. One is to gain mathematical fluency. The other is to find the physics in the mathematics. Slogan: "Do all the problems."
3. One of the aspects of the seminar experience that took me the longest to learn was the utility of asking a question. If you encounter difficulty, carefully formulate a question (often the question answers itself in this process!), then ask someone. If this person is madly preparing a midterm or a bernaise sauce or does not know the answer, try someone else. In particular do not hesitate to ask me. If all else fails, go on to other problems and return to the question later. The slogan is: "Minimize frustration!" [A few years ago Seth rented a moving truck from "No Hurts Rental." On the wall someone hung a sign for frustrated people. It had a large circle on it. In the middle were printed the words, "Bang Head Here". This is a very bad idea. Metaphorically or not, there is very little gain in working on a problem to the point of head-banging frustration. Ask questions first!]
4. When writing solutions keep in mind that there is also a large difference between sketching a solution on your napkin at dinner and writing up the solution so that someone can read it (that may include you!) As with much writing, keep your audience in mind. Keep your classmates in mind but also try thinking of yourself in 3 months.
5. Much of what is true for solutions also applies to presentations. Clearly state the issue or problem, outline the tools needed, and proceed providing information when needed. Feel free to skip algebraic steps once you have cleared it with the class. Show us (including me) something we don't already know, e.g. a new numerical solution or a experimental manifestation of a problem. Slogan: "To do well: Be clear. To impress, exhibit novelty."
6. The best policy is to prepare fully for seminar before we meet and write up summaries and/or complete solutions after the actual seminar. It is not easy to keep up. But your notes will be loads of help for graduate school classes, qualifying exams Think of this as writing up a book from which you can relearn the subject.
7. It is never too early (or too late) to start being clear about what you understand and what you do not. There is a vast, amorphous plain between familiarity and understanding. Question your own understanding by trying it out on new situations. If your knowledge is not what is required, find the difference and learn from it.
8. If you haven't already started, start keeping a sheet of paper with useful formulae so you can quickly answer questions such as, what is the spherical coordinate area element?