lagrangian
rallain | December 6, 2009Looking back at part I of this idea, I don't think I did a very good job. Let me summarize the key things I wanted to say:
Normally, there are two ways of modeling the motion of an object:
Calculating the forces on the object and using the momentum principle or Newton's second law (which are the same thing). I called this the Newtonian way. The problem with this method is forces that constrain the motion (like the normal force). These forces have a variable magnitude to make the object stay on a particular surface.
Defining some variables that describe the system as it is constrained.…
rallain | December 4, 2009This post has been sitting in my mind for quite some time. Really, it is about mechanics - not about pendulums. What is the goal in mechanics (classical mechanics, if you like)? Generally, it is to find out how something changes over time. If you could get an equation of motion, that would do it.
As Matt (Built on Facts) did a while ago, it can be shown that you can get the equation of motion for a mass on a spring with normal Newtonian mechanics or with Lagrangian mechanics. Let me summarize two different ways of looking at the motion of an object.
The Newtonian Way
Maybe that isn't the…