Harmonic Oscilator
mspringer | December 2, 2009A few days ago we looked at what a Lagrangian actually is. The short of it is that it's the kinetic energy minus the potential energy of a given mass*. More importantly, if you construct the classical action by integrating the Lagrangian over the time (see the previous link for a more full explanation) you'll find that the actual trajectory is the one that minimizes the action.
It turns out that the way to find the path that minimizes the action is pretty easy. In honor of two of its pioneers, we call it the Euler-Lagrange equation. If you can find a solution that satisfies the Euler-…
mspringer | November 26, 2009First of all, happy Thanksgiving everyone! I hope you spend the day happily with the people you care about, and remember to spend a moment or two reflecting on the things for which you're thankful this year. Now on with the show:
Back when I first started writing this blog, I focused mostly on problem solving. The goal was to bridge the gap between popularization and textbook. I was always doubtful there was much of a market for this, but of course there are at least some interested people and especially since writing is so fun I was and am I'm more than happy to fill that gap. Over the…