APPH E3200x Site Information

Welcome to the APPH E3200x class information site.

Classical mechanics intended for junior level applied physics students. Emphasis is placed on teaching fundamentals through applications, both historical and contemporary. The applications will also serve to illustrate the connections between the mathematical methods of classical mechanics and other areas of science. Finally, experimental examples will be given which indicate the limitations of classical dynamics and motivate modern physics.

This year's course will also introduce students to computational physics through the solution of a variety of interesting problems in classical mechanics. AP E3200x does not require prior programming experience. By the end of the semester, students will be comfortable in the construction and solution of ordinary differential equations (ODEs) to describe mechanics. Modern desktop scientific computing allows students to visualize complex solutions and to confirm algebraic solutions.

Mechanics is both a fundamental branch of physics and an essential skill for design, manipulation, and control of modern technology. Mechanics underlies all engineered systems, and the techniques developed in mechanics can be applied to analogous electrical systems.

The usual pre-requists for AP E3200x are:

• PHYS W1401x Introduction to mechanics and thermodynamics
• PHYS W1402y Introduction to electricity, magnetism, and optics
• MATH V1201x or y Calculus, III

Also very useful is MATH V2030x or y Ordinary differential equations or APMA E2101y Introduction to Applied Mathematics.

Key topics covered include:

• Linear and nonlinear oscillations, the pendulum, and deterministic chaos
• Gravitation and Kepler's laws of planetary motion
• Coupled oscillators and "waves"
• Hamilton's Principle and Lagrangian and Hamiltonian Dynamics
• Motion in a rotating (noninertial) frame
• Dynamics of Rigid Bodies (and angular momentum and the inertial tenor)

The goal of this course is to provide a solid understanding of both the mathematical formalism of applied mechanics and to introduce students to applications of mechanics to modern engineered systems.

The primary course textbook is Classical Dynamics of Particles and Systems by Stephen Thornton of University of Virginia and the late Jerry Marion of University of Maryland. This is an excellent text for mechanics, and we will be following the outline of textbook in the course. The Amazon.com link to a student guide is available here. (Please note: purchase of these books is not required.) Columbia students have access to an eBook copy of the 1st Edition of this book.

I will occasionally refer to other textbooks, including Introduction to Mechanics by Dan Kleppner and Robert Kolenkow. Among the most famous textbooks in mechanics are Classical Mechanics by Columbia professor Herbert Goldtsein and Mechanics by Russian physicists Landau and Lifshitz.

Everyone should have access to this textbook, and this semester's syllabus will follow many parts contained in the entire book.

I will present numerical illustrations of plasma physics using Mathematica. Mathematica is available to all students through Columbia University.

Feel free to contact me, Prof. Mike Mauel, anytime. I also try to answer my emails frequently. If you have have question (even if you're stuck on a homework problem), send me an email.

Lectures will be held every Monday and Wednesday afternoon, 1:10-2:25 PM, in Room 327, S. W. Mudd Building.

A student's grade for the course will be based primarily on two closed-book quizes (25%) and one final exam (50%). The quiz dates will be October 5 and November 16.

I will also assign weekly homework assignments but these homeworks will be discussed in class. They will not count on your final grade. Participating in these homeworks will be the most important action you can take to learn the material. Homeworks are due at the beginning of the following class period and will be discussed.

This Web Site is a convenient resource for APPH E3200x. (I will also link to materials on the Columbia CourseWorks site for APPH E3200x. After logging into to CourseWorks, you must select "AP 3200" to view and download materials.)

• Wikipedia's page for Mechanics (which has a nice historical overview)
• Stanford's Leonard Susskind (born and raised in New York City and creating founder of "string theory") recorded a short course on Classical Mechanics available on YouTube:
  • (September 26, 2011) Leonard Susskind gives a brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles.
  • (October 3, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on some of the incorrect laws of motion that were first proposed by Aristotle. While they are invalid they provide some insight into how modern physics has developed to the state it is at today.
  • (October 10, 2011) Leonard Susskind discusses Lagrangian functions as they relate to coordinate systems and forces in a system.
  • (October 17, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses symmetry and conservation laws, including the principle of least action and Lagrangian methods.
  • (October 24, 2011) Leonard Susskind discusses different particle transformations as well as how to represent and analyze them using tools like the LaGrangian.
  • (November 1, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on the motion of objects. He starts with a general example of a wedge on a frictionless plane and uses it as the building block for more complicated theory.
  • (November 7, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on Liouville's Theorem, which he describes as one of the basis for Hamiltonian mechanics. He works to prove the reversibility of classical mechanics.
  • (November 14, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he looks closely at the concept of angular momentum and Poisson Brackets. He derives the basic angular momentum equations and shows how they can describe this fundamental type of motion.
  • (November 21, 2011) Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he dives into the topics of magnetic and electrostatic forces. He derives these forces to show their relationship to magnetic fields and potential.
  • (November 28, 2011) Leonard Susskind wraps up the lecture series by finishing his talk on particles and both electric and magnetic fields and how they relate to physics.
• The world's most accurate clock
• NASA's orbital debri map and information

Since Fall 2004, I have decided to keep a "weblog" (also known as a "blog") about my academic work. When I started, the weblog was intended only for APPH E4010x Introduction to Nuclear Science. I am not sure if anything important will be recorded there. The blog is like an instructor's diary. Based on my experience from last year, the weblog was essentially unused by students except for the occasional glance. (Students are too busy to read this stuff, and I'm too busy to write anything interesting!)

Nevertheless, the link to my (personal) course blog is here. I am not promising to provide frequent updates.

I also have a link to this page from Columbia's CourseWorks site under the APPH E3200x links.