Looking at a path of system state (x(t),v(t)) as a vector, the Lagrangian strangely is a scalar function of pairs of coordinates of the vector.
If, on the other hand, the complete state of a system was captured in a single complex number x+iv, a complex analogue of the Lagrangian would simply...
I try to find errors or contradictions in the book; if the book is good, then when I find one it usually means I've misunderstood something until I prove myself wrong.
Calculus is the language of change, and physics describes how nature changes, so physics sans calculus won't give you much insight into nature except for situations with no change.
Everyone, thank you so much for your replies, twofish-quant especially.
I know, I just don't want to be completely clueless. I want to understand everything to the point of being able to ask thought-provoking questions. And by everything I mean a handful of other fields.
The truth is that...
OP: I think you were looking for something more fundamental.
The form of the Lagrangian follows from constraints we assume the laws of physics must obey in classical mechanics.
First, assume that there exists a frame of reference in which space and time are homogeneous and isotropic; this is...
They're the ones behind Physics Today, actually, to which I am now subscribed. :)
By depth I mean how well the results are connected to first principles. If they're just presented as facts without some understanding my mind rejects it like a blood transfusion of incompatible type.
Schroeder's...
So I want to be a physicist.
Avoiding false modesty, I'm pretty good at it, probably the best in my year in physics and possibly math. I never have problems learning, unless the material is shallowly presented and I reject it, which has happened in many of my classes, unfortunately. I've taken...