AlephZero,
I guess you copied the wrong ode :( - its sigma_z and not sigma_x in the problem.
However, something similar could work with the actual ODE. The second order equation there takes a slightly more complicated form:
\nu\ddot x-\dot\nu\dot x-[\dot\nu+\nu+2\nu\dot\nu]x = 0...
Ben Niehoff, this is a nice way of rewriting the ansatz. One sees immediately that r_0 has to vanish, since the identity matrix is not present in the rhs of the ODE.
However, there are two major problems with it:
As a solution to the ODE, x(t) has to reproduce itself (modulo factors)...
Hi all!
Thanks for your replies!
matematikawan, I guess it doesn't work with a loop, since it gives the error message:
Error: Expression or statement is incomplete or incorrect.
MATLABdude, I think the problem is not in the type of multiplication, here's an example which cannot be...
Hi, AlephZero!
If we assume that x(t) is periodic and indeed expand it in Fourier series (vector-valued coefficients a_n), to compare the coefficients, the rhs has time dependent coefficients, so we get so solve an equation of the form
in*a_n = G(t)*a_n - for some matrix G(t) I think I...
Hi all!
I'm trying to solve the following system of ODE's, but somewhat unsuccessful...
\dot \vec x = [-i\omega(t)\sigma_z - \nu(t)\sigma_y]\vec x
with sigma_i the Pauli matrices and w(t) and v(t) well-behaved functions of t (actually I also have that w = 1+v). Nevertheless, v(t+T) =...
Hi all!
I am having great trouble in the last days trying to make MATLAB plot for me a function of a matrix exponential of a variable t.
Here's my attempt:
first, I define the z-Pauli matrix s_3 and the identity matrix I by:
%define the pauli matrices and the identity I%
I = [1 0; 0...
Hi all!
I attempted to solve Airy's equation
http://en.wikipedia.org/wiki/Airy_function
\ddot y = \lambda ty
in a rather nontraditional way which I highly doubt to be correct for obvious reasons, but I can't find my mistake. Here's my attempt:
first, rewrite the second order ode as a...
Hi all!
Just because,Master J, you mentioned you're using the residue thm in this case to evaluate an integral, here's an amusing question for you about an integral of a similar type:
First, x is still a non-negative number. We are interesting in the integral over all R of...
ODE's = Ordinary Differential Equations
PDE's = Partial Differential Equations (much harder)
They are both needed ubiquitously in physics. Every equation of motion is a differential equation, since it has to predict the rate of change of some quantity in/of the system. (evolution of a...
Hi, Matthew!
Welcome to Physics Forums!
It's great you're so enthusiastic about Einstein's General Relativity (GR) and theoretical physics only at the age of 17. It's also a very good decision to post a thread in the forum, since you're going to get many different answers and suggestions...
Ok, so suppose the gravitomagnetic eqn's, as stated in the article, are a valid approximation under some physical conditions, whatever they may be.
There's still a wave equation arising from them, which accounts for the description of radiation in this particular limit.
Clearly, it's not...
Hi all!
I was browsing Wikipedia when I came upon the following article:
http://en.wikipedia.org/wiki/Gravitomagnetism
It seems here they state a form of the complete linearized Einstein equations that resembles very much (or is mathematically identical to that of) Maxwell's equations...
yeah, yeah, that's clear.
I was just wondering if anyone had experienced this and how he went about it.
As to the 'unfairness'.. well, that's a general fact of life, so nothing really new here :rofl:
So, what do international students do, if they cannot cover the minimum standards for obtaining the visa and prove that they have sufficient money to finance their first year in grad school?
I mean, $ 50 000 is a lot of money. A 22-24 year-old student coming from a developing country...