ATAR Notes: Forum

Uni Stuff => Science => Faculties => Physics => Topic started by: QuantumJG on May 18, 2010, 08:18:41 pm

Title: Lagrangian problems
Post by: QuantumJG on May 18, 2010, 08:18:41 pm: Ok in classical physics we have been using Lagrangians to solve physics problems, but I'm lost.

How can you determine what constants of motion there are?

In lectures we looked at the Kepler problem as an example and he used the Hamiltonian to show the Lagrangian was independent of time:

$r^{.} \dfrac{\partial L}{\partial r^{.} } + \theta ^{.} \dfrac{\partial L}{ \partial \theta ^{.} } + \phi \dfrac{ \partial L }{ \partial \phi } - L = constant$

But I don't know how to prove this!!!
Title: Re: Lagrangian problems
Post by: mark_alec on May 18, 2010, 09:28:01 pm: If you write out the Hamiltonian (total energy) and apply the appropriate formula to dH/dt, you will see that as it is a conservative system, the total energy is constant and so dH/dt = 0. It follows that the Lagrangian must be independent of time.

If that answer doesn't satisfy you, could you post some of the working out and formulae, as I don't remember the specifics?
Title: Re: Lagrangian problems
Post by: QuantumJG on May 18, 2010, 09:40:27 pm: Ok thanks.

Did you find thermal and classical much more difficullt than Quantum Mechanics and Special Relativity? In QM & SR my lowest mark is 80% (so far) and for Therm & class my lowest mark is too embarrasing.
Title: Re: Lagrangian problems
Post by: mark_alec on May 18, 2010, 10:17:49 pm: Yes, I found classical mechanics much more difficult than quantum or special relativity. It is hard subject matter but it should click with you after some time and thought.