2011-02-21, 05:56 AM
When you 'input' how your particles are constrained to move and what their initial potential and kinetic energies are, Lagrangian mechanics will basically spit out a time variable acceleration vector. That's how it's solved, by telling you what kind of fucked up acceleration each particle undergoes. Honestly, if you aren't a physics major (or don't wanna be), it's probably not worth the time. If you are, this and introductory GR were by far my 2 favorite physics subjects. But like I said, junior in college level.
Your other thread looks like something you wouldn't need Lagrangian mechanics for, because you don't constrain the particle's occupiable space to a subspace of whatever set of dimensions you're working in. An asymmetric newton's cradle can only swing back and forth, and it'll probably be chaotic (which is why introductory mechanics courses don't do it), but the balls aren't going to detach from the frame. So... More like Lagrangian mechanics is a branch of the other thread, where you would say your particle is a bead on a fixed string / restricted to a hula hoop / something like that. You could apply the concepts in the other thread to this and probably wouldn't be able to do some harder Lagrangian stuff without them.
Your other thread looks like something you wouldn't need Lagrangian mechanics for, because you don't constrain the particle's occupiable space to a subspace of whatever set of dimensions you're working in. An asymmetric newton's cradle can only swing back and forth, and it'll probably be chaotic (which is why introductory mechanics courses don't do it), but the balls aren't going to detach from the frame. So... More like Lagrangian mechanics is a branch of the other thread, where you would say your particle is a bead on a fixed string / restricted to a hula hoop / something like that. You could apply the concepts in the other thread to this and probably wouldn't be able to do some harder Lagrangian stuff without them.