Recent content by ellipsis

Answering the title: Yes. It's weak in the context of the four fundamental forces: gravity, electromagnetism, "strong nuclear, weak nuclear", the last two of which are just forces which keep atoms together. The key to understanding: Playing with magnets, you can easily see how...

How is it the case people simulate arbitrary mass-spring systems, then? I'm considering taking the approach of approximating pendulums by springs with arbitrarily high spring constants, but the problem becomes 'stiff' in that case, and requires low time-steps. A hundred terms in my Lagrangian...

I want to see how a pendulum system with, say, n=100 works. There has to be a way to "generalize" the behavior of one component of a pendulum given the components it is immediately attached to.

Thanks for your response! The small angle approximation is not something I'm interested in (All of this is due to wanting to see how pendulums really work), but I'll keep that in mind. Do you know anything about calculating equations of motion in Cartesian coordinates?

Hey all. I've been experimenting with Lagrangian mechanics (and numerical simulation of physical systems), and I've come across a problem. By finding the Lagrangian, then using the Euler-Lagrange formula, I can find equations of motion (in generalized angular coordinates with respect to the...

By "the empirically established upper limit is very small" only means we've proven it is less than a certain size. This says nothing about our established empirical lower limit, which is zero. He is saying: "Everything else is on the scale of 1, 2, 3. We have proven a photon's mass is less...

At the scale of a cubic meter. Does it not make sense to ask how many photons are in a cubic meter on Earth in a normal room?

'why' - You can't explain small things with big things, just like you can't explain addition in terms of multiplication (but you can vice-versa). 'Why' is one of those big things. As far as figuring out facts, though: We recognize patterns (equations) and extrapolate them to the situations we...

It seems to me that light travels (in a room) from everywhere, to everywhere else: A complicated, messy, interconnected network of photons of varying wavelengths which somehow avoid ever colliding with each other. This is what allows me to see things, and other people to see other things...

I was going to attach a .gif animation of the simulation, but I couldn't get it to work. The trajectory of the end mass is fairly smooth, but the first and second masses bounce around wildly relative to each other, and attain quite high velocities (but total energy is constant). When I get...

Is a triple pendulum with a significantly heavy end-mass supposed to spaz around? Using the Euler-Lagrange formula in Mathematica, I've found (and simulated http://poteat.github.io/triplependulum.html) a triple pendulum system with arbitrary masses and lengths. The rods are massless (so no...

Ah, my mistake. In that case, what exactly did phind's mean when he said energy conservation doesn't apply on cosmological scales?

To expand on that, light loses energy more and more (turns red, redshift) as it travels further and further through space. Well, I believe it has something to do with the relative distance and speed of stars, but either way, the energy is lost. Someone please correct me if I'm wrong.

This is delightful, but I think people need a little more clarification before they can answer that question. What sort of thing is it?

Ha! I've found it! If the maximum Euclidean distance between any two vectors in the set ##S## is below or equal to ##2k##, then ##S## can be enclosed by a circle of radius ##k##! Therefore, there exists a point which is equal to or less than ##k## from every element in the set ##S##! This is...