Conservation of the Laplace-Runge-Lenz Vector

fisica1988
Messages
2
Reaction score
0
Hmm...Latex doesn't seem to be working at the moment...

How does one show the conservation of the Laplace-Runge-Lenz (LRL) vector using the Hamiltonian of the two-body system? Showing it's conserved otherwise it's not hard. You can take the time derivative of the LRL vector and show that it's zero or a couple other ways which I worked out before (I would type it out but Latex seemingly disabled makes it tedious and cumbersome). The one thing I can't figure out is how to get the conservation of the LRL vector from the Hamiltonian of the two-body system. What I did was take the square of the LRL vector and find the energy from that but then it becomes uncertain.
 
Physics news on Phys.org
You know how to calculate commutators?
 
Ah yes yes, thank you, I got it now.
 

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Thread 'Help to convert units of a simple formula'

The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
View full post »

Similar threads

Conservation of the Laplace-Runge-Lenz vector in a Central Field
Replies
3
Views
2K
Symmetry behind Laplace-Runge-Lenz vector conservation?
Replies
7
Views
10K
What is Laplace-Runge-Lenz vector
Replies
1
Views
6K
Laplace-Runge-Lenz vector problem
Replies
2
Views
3K
Laplace-Runge-Lenz Vector for Magnetic Monopole
Replies
1
Views
5K
From noether theorem to Laplace-runge-lenz vector
Replies
3
Views
5K
Finding the Energy of an Outgoing Particle in a Momentum Conservation Problem
Replies
2
Views
2K
B Ignoring the motion of the Earth for energy vs. momentum conservation
Replies
21
Views
2K
How does the Runge-Lenz vector explain accidental degeneracies?
Replies
17
Views
6K
Wrong solution order using Runge Kutta 4
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top