Compute the canonical momentum

  • Thread starter Thread starter Lambda96
  • Start date Start date
  • Tags Tags
    Momentum Physics
Click For Summary
The discussion centers on calculating the canonical momentum from the given Lagrange function, which is expressed as L = (1/2)m||dot{x}||^2 + (q/c) dot{x} · A - qφ. The user correctly derives the canonical momentum as π = m dot{x} + (q/c) · A. There is a question about whether the symbol for canonical momentum should be bold, indicating a potential formatting issue. The user acknowledges the oversight in not using the bold notation for π. Overall, the calculation appears to be correct, with a focus on proper representation.
Lambda96
Messages
233
Reaction score
77
Homework Statement
Compute the canonical momentum ##\pi=\frac{\partial L}{\partial \dot{\textbf{x}}}##
Relevant Equations
none
Hi everyone,

I am not sure if I have calculated task b correctly:

Bildschirmfoto 2024-11-13 um 20.16.55.png


The Lagrange function has the form ##L=\frac{1}{2}m\Vert \dot{\textbf{x}}\|^2+\frac{q}{c} \dot{\textbf{x}} \cdot \textbf{A}-q\phi##

I then formed the canonical momentum ##\pi=\frac{\partial L}{\partial \dot{\textbf{x}}}##


$$\pi=m \dot{\textbf{x}}+\frac{q}{c} \cdot \textbf{A}$$
 
Physics news on Phys.org
Lambda96 said:
I then formed the canonical momentum ##\pi=\frac{\partial L}{\partial \dot{\textbf{x}}}##

$$\pi=m \dot{\textbf{x}}+\frac{q}{c} \cdot \textbf{A}$$
Should ##\pi## be bold (##\pmb{\pi}##)? Otherwise, it looks good to me.
 
  • Like
Likes Lambda96 and PhDeezNutz
Thank you TSny for your help 👍

Unfortunately I had forgotten to write ##\pmb{\pi}## :smile:
 
I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
19
Views
2K
Replies
9
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K