Recent content by LoopQG

Homework Statement Given a matrix {latex] A_11 =A_22 = 0 A_12 =A_21 = x/y +y/x [ /latex] Find the contravariant components in polar coordinates. Answer: [itex] A_11 = 2 A_22 = -2/r^2 A_12 = 2cot(2 /theta)/r [ /latex] Homework Equations I used the polar coordinates metric to raise...

Homework Statement I need to calculate S in order to calculate the perihelion shift of Mercury. I have found the Euler Lagrange equation to be: G^{\nu\beta}(\partial_{\beta}S)(\partial_{\nu}S)-m^{2}=0 Which is a form of the Hamilton-Jacobi equation. Which my professor tells me is...

Thanks a lot for the help, I ended up assuming a small \theta then expnding and I get the right answer.

The angle from the vertical axis of the sphere, grcos(\theta) is the gravitational force at that point

Do you mean take dU/d\theta which equals \sqrt(2gR)(1/2)(1-cos(\theta))^(-1/2) sin(\theta) but then integrating that don't i just get the same thing back? If not at what point should I consider integrating. I see where you are going with this because the flow velocity is zero at the...

Homework Statement Consider a spherical bubble of radius R,rising in water. Using Bernoulli's equation show that the rate of rise of the bubble is: U=(2/3) \sqrt(gR) Homework Equations Bernoulli Equation Potential Flow The Attempt at a Solution I have considered the...

you are so close remember sin(45)=cos(45)=1/sqrt(2) so sin(x+45)=1/sqrt(2) [sin(x) +cos(x)]

f'(x)=1+[f(x)]^2 so f(x)=x+[f(x)^3]/3 so take f'(g(x)) following the rule stated f'(g(x))=1 + x^2 = 1/g'(x) notice also f'(g(x))=1 so g(x) must subtract out that x^2 hope this helps

This isn't a HW question just something I am curious about. I was looking on wikipedia and found a way to prive the Levi-Citiva Kronecker Delta relation that I hadn't seen before. The site claims \epsilon_{ijk}\epsilon_{lmn} = \det \begin{bmatrix} \delta_{il} \delta_{im} \delta_{in}\\...

excellent. hanks so much for your help. I do have one more question though. The idea behind this was to find the principal axes of the strain rate tensor, which is the matrix in post 1. And find the principal rates of strain. For the principal rates of strain i am getting from my text that I...

ok so after figuring out i had to normalize i first chose x=1 so z=-3 +sqrt(10) for 5/2 + sqrt(5/2) and for 5/2 - sqrt(5/2) i set z=1 and x=3-sqrt(10) and y=0 for both can you verify if this is correct? thank you for all the guidance.

Yes but what about the vectors for the other values. I still get all the components equal zero. I have plugged it into MATLAB and i know what the other eigenvectors are but i don't see how to get them analytically

Homework Statement Find the eigenvalues and eigenvectors of this matrix. [4 0 1/2 ] [0 -5 0 ] [1/2 0 1 ] [b]3. The Attempt at a Solution I have found the eigenvalues = -5, 5/2 + sqrt(5/2), 5/2 - sqrt(5/2) I know to get the eigenvectors you subtract the...

Thanks Ben, I'm new to physics forum didn't know you could do that, appreciate the help!

Find the Euler – Lagrange Equation when L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4 Use g_u_v to raise/lower indices D_p is the covariant derivative I am very new at this notation and am having a lot of trouble getting anywhere with this. I know I have to take the action: S = \int Ldt...