Struggling with 3-D Hamiltonian for Variational Principle Integration?

Airsteve0
Messages
80
Reaction score
0
attachment.php?attachmentid=43825&d=1329086791.png

Homework Statement


The problem statement is a bit length so I have attached a picture of the problem instead. The issue I am having pertains to part (b).


Homework Equations





The Attempt at a Solution


The main issue I am having is with what my Hamiltonian should look like when I do the integrals for part (b). Since the problem is in 3-D I'm just second guessing everything I write down. Any assistance is greatly appreciated.
 

Attachments

  • Untitled.png
    Untitled.png
    52.7 KB · Views: 631
Physics news on Phys.org
nvm got it
 

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

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 »

Similar threads

Getting geodesic from variational principle
Replies
2
Views
1K
Upper bound for first excited state - variational principle
Replies
2
Views
2K
Lagrangian/Stationary-action principle
Replies
5
Views
1K
How to show that ##f_i(q_i, p_i)## is constant
Replies
6
Views
1K
I Different Approaches to the Time Dependent Variational Principle
Replies
0
Views
1K
How Does Hamilton's Principle Lead to Lagrange's Equations?
Replies
1
Views
2K
What is the Variational Principle for Estimating Energy of First Excited State?
Replies
1
Views
2K
I Integral in a variational principle problem
Replies
3
Views
2K
Thermodynamics: deriving expression for S = S(T, V, N) - constant problems
Replies
19
Views
2K
A Can position and velocity vary independently in Hamilton's Principle?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top