Physics Links 1 - The LagrangianJuly 14th, 2019
For no particular reason other than that understanding why things happen is fun, I'm teaching myself physics. Obviously, I don't have anything interesting to say on the subject—I'm a beginner. However, I can gauge whether or not resources are helpful in improving understanding. This post contains the first installment of resources. I am assuming knowledge of a year of introductory physics, simply because that is where I am.
I am studying David Morin's Introduction to Classical Mechanics, and as of Chapter 6, I have found it to be excellent. The explanations haven't failed me yet, and the problems in each chapter are outstandingly difficult. A draft of this chapter is available from the author.
The topics presented are the Lagrangian, and the principle of stationary action. Feynman's explanation helped me understand why we are interested in the lack of first-order changes in the Lagrangian:
"If there is a change in the first order when I deviate the curve a certain way, there is a change in the action that is proportional to the deviation. The change presumably makes the action greater; otherwise we haven’t got a minimum. But then if the change is proportional to the deviation, reversing the sign of the deviation will make the action less. We would get the action to increase one way and to decrease the other way. The only way that it could really be a minimum is that in the first approximation it doesn’t make any change, that the changes are proportional to the square of the deviations from the true path.
The term holonomic is not mentioned in the book, yet came up several times when I was looking for more detail on constraints.
Finally, I couldn't find an intuitive explanation of Noether's theorem that was clearer than the book's explanation.
That's all for this week—please tweet me with comments.