Ooh thank you Erythro, that's a great summary not just for this but all my Lagrange problems. I was a bit overwhelmed by pages of subtly different examples and needed just what you gave: a template for how to address a problem generally.
The only thing I don't understand now is how to get a...
Homework Statement
A particle of mass m moves in a potential of the form
U(r) = (1/2)kr^2
k = const greater than zero
1) Determine the possible orbits r = r(theta) and show that they are closed
2) Solve the equations of motion (although it is sufficient to derive the time...
Homework Statement
We're required to analyse a particle moving in the potential U(x) = a/x^2 (a > 0). Setting F = U(x) and using the Newton equation F = ma, this gives rise to the DE:
d2x = a/m * (1/x^2)
dt^2
I can't for the life of me figure out what method to...