Recent content by vputz

Okay, I thought about it a bit more, and there are a couple ways forward. Thinking abstractly, we have something shaped like this: \frac{dx_1}{dt} = f(t)\left( g(a_1)-h(x_2-x_1)\right) \frac{dx_2}{dt} = -f(t)\left( g(a_2)-h(x_2-x_1)\right) In our case, g(a) is constant over time, while...

...sadly, the above works brilliantly for simple stokes velocity when everything is nice and linear, but the introduction of the cross-terms means this doesn't work (so the idea of a "stationary point on the dumbbell" seems invalid, or that it moves over time so dy/dt above is not zero). Hmm...

My latest idea, which may work: Define some point on the line between x1 and x2: x_{cm} = x_1 + y( x_2 - x_1 ) Then say that this point doesn't move, set d/dt of it to zero, solve for y; since we know d/dt of x_1 and x_2, this may work (I'm imagining that y does not change with time...

A sphere heads east from Los Angeles... ("centre of hydrodynamic 'mass'" problem) Homework Statement This is actually from research, but it's one of those "this should be an easy problem and I'm wasting too much time making it too difficult" problems, so I thought it fit better under...

We used a device very similar contracted through Workhorse Technologies to map a cave, and I was able to use the derived data set with the http://www.cs.utexas.edu/~amenta/powercrust/welcome.html algorithm to whip up a shell that could be transformed and imported as a Quake map, although...

The Attempt at a Solution In 3d, things start going wrong. We can basically extend constraint (1) fairly trivially: J=[ 0, 0, 0, x_{2}-x_{3}, y_{2}-y_{3}, z_{2}-z_{3}, x_{3}-x_2, y_3-y_2, z_3-z_2] ...but the collinear constraint is trickier (to me). So far my attempts have centred around...

Homework Statement I'm trying to write a Lagrange-multiplier constraint simulation along the lines of those described by Andrew Witkin here. The basic idea for this simulation is that you have a number of objects represented by three collinear beads joined by massless rods; one of the...

Homework Statement Okay, this would be easy if it hadn't been 15 years since undergrad quantum. Here goes. I'm finding the energy spectrum of a Heisenberg "two-electron ferromagnet", if you will, with a Hamiltonian described by H=-J\hat{S_1}\cdot\hat{S_2}-h(\hat{S_{z1}}+\hat{S_{z2}})...

Boggle boggle boggle... hmm, I'll play with it if I have time. Thanks! (I "solved" that problem about 4/5 of the way by brute force--actually calculating matrices and their commutators; hooray for Maxima. But I'd like to do it the right way. Sure wish I knew how to make a CAS like Maxima...

Well, I would certainly like it to be so! But when I expand the right hand side of the second way, I get terms looking like \eta^{\nu\rho}S^{\mu\sigma} = \frac{i}{4}(\gamma^{\nu\rho}+\gamma^\rho\nu)[\gamma^\mu,\gamma^\sigma]. Writing those out, I seem to get the terms (again, writing...

Homework Statement As part of a problem set, I'm trying to show that the S^{\mu\nu} matrices defined by S^{\mu\nu}=\frac{i}{4}[\gamma^\mu,\gamma^\nu] constitute a representation of the Lorentz algebra. Well, luckily P&S assure me that by repeated use of...