August 26, 2003

Physics 208 and 303: Classical Mechanics

A special introduction for Physics 303,
motivated in part by some of your hand-written remarks on the 208 class evaluation forms.

My impression i that there may be some confusion about what is this course we call Classical Mechanics; and why is might not have been what you expected.

Today we use the term “Classical Mechanics” to mean “not Quantum Mechanics”; in both cases however the word “Mechanics” can be misleading. In both cases we mean a theory which explains motion of objects, interaction of objects, and the structure of objects. What differs between the two Mechanics is the scale of sizes at which they apply. But in both cases we mean an introduction to the mathematical background required to understand motion, interaction and structure. Classical Mechanics has little to do with solving the Newtonian equations of motion; it has much to do with developing methods which use the concept of energy rather than the concept of force, through the definition of the Lagrangian- and the Hamiltonian functions. In fact the important accomplishments of Classical Mechanics are the Lagrange- and Hamilton's  equations of motion. What might ultimately strike you is their simple beauty and economy of expression; but perhaps more important than their beauty is their universal application to other fields of theoretical physics, in particular Electromagnetism, Quantum Mechanics and Field Theory; the first two are going to be your next step of learning of the mathematical characterization of motion, interaction and structure.

In my view you should not be completely distressed by the fact that we discussed problems which did not seem to have direct relevance to your everyday experience or interest. Physics 208 was your first step into theoretical physics, and what you have learnt here will find many applications, will be the object of further developments and refinements in your very near future. I regret to have to say: “never mind that you could have solved some of the problems more quickly, with less work, simply using Newton’s 3 laws”. You in fact had already learned most about Newton’s law in Phys 101. But the Lagrange/Hamilton equations have much farther reaching consequences. I hope you will keep alert and remain excited about the possibilities ahead, which will be based on what you have learned in Classical Mechanics I and II.

C.F. Perdrisat