Some interesting (to me, anyway) thoughts on Classical Mechanics

[mahf]

Well, I got home a little while ago from campus. I went today to turn in Johannah's final paper for her Milton class, since she didn't have time because of work, plus I had to go finish and turn in my last homework assignment for classical mechanics today. I have to say that I have really enjoyed classical mechanics. Dr. Biswas is a very good

Comments

[mahf]

Well it isn't really about measurements per se. Its like this. Instead of adding up all the forces, you just write down "equations of constraint" and you write down the kinetic and potential energy. The secret is that the forces are *contained* within the equations of constraint and the potential energy. But its mathematically MUCH easier to calculate the potential and the constraints.

All three formalisms are in the end equivalent. But the Lagrangian and Hamiltonian are much more general. For example, in Newtonian mechanics, you have to use some coordinate system about some origin. But for the Lagrangian, let's say you were calculating the motion of a wheel rolling down a hill. For Newtonian methods, you'd have to work from some fixed axis. WIth the Lagrangian, you could pick the angle the wheel has rolled through and the vertical distance it has traveled as your two coordinates. You don't have to add any vectors, you don't have to worry about the coordinates being orthonormal, just pick the things that are important in the given case. The power comes from the universal applicability.

Anyway, hope that explains a little bit.