A question about Hamilton's principle

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It's an integral principle which concerns itself with the motion of a mechanical system, but is more commonly expressed in its differential form as a principle of least action. Does anybody know why?

― 30 Bangin' Tunes That You've Already Got ... IN A DIFFERENT ORDER! (Barry Brune, Tuesday, 19 July 2005 02:33 (twenty years ago)

Cause people can never remember the difference between Hamilton and Lagrange?

― Rufus 3000 (Mr Noodles), Tuesday, 19 July 2005 02:35 (twenty years ago)

Or maybe it's just me, cause all I ever remember is the Lagrangian is classical mechanics as opposed to what Hamilton proposed. Are you being serious cause I can dig out the notes if you want.

― Rufus 3000 (Mr Noodles), Tuesday, 19 July 2005 02:37 (twenty years ago)

I forget why (its almost midnight and I should be in bed) Lagrange had some great idea to improve upon Newtonian physics that the Lagrangian L = kinetic minus potential energy. So that force is the negative of the [partial?] derative of the potential energy over an r vector.

Hamilton changed the velocity to momentum which would later account for relativistic effects.

Nice to see I remembered something, just not the important parts. Why the sudden interest in 200 year old theories?

― Rufus 3000 (Mr Noodles), Tuesday, 19 July 2005 02:57 (twenty years ago)

DAMN YOU ZAC

― 30 Bangin' Tunes That You've Already Got ... IN A DIFFERENT ORDER! (Barry Brune, Tuesday, 19 July 2005 03:21 (twenty years ago)

This was my thread pachinko entry.

― 30 Bangin' Tunes That You've Already Got ... IN A DIFFERENT ORDER! (Barry Brune, Tuesday, 19 July 2005 03:23 (twenty years ago)

Is the fact that the particle will be following the greatest drop in potential energy going to lead it to through the shortest path possible until all the energy in the system has converted to kinetic?
I know I've got all this in a little blue binder somewhere.

You want the proof? You can't handle the proof!

― Rufus 3000 (Mr Noodles), Tuesday, 19 July 2005 10:23 (twenty years ago)

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