Recent content by Anachronist

Wow, that's incredible, and far more than I expected. Really helpful to see a plot of the isosurfaces, as well as a not-terribly-complicated solution for p=1. To your last question, yes, that impacts the utility of this approach, because it isn't quite what I expected to see. I was going for...

Yes, that is exactly what I came up with for the charge density with respect to z. And last night while falling asleep I imagined an integral similar to what you describe. I am wondering if there are certain values of p for which this is simpler and closed form. Because this is for generating...

Yes, that was sloppy language on my part. I erred in calling it a "wire", I meant a 1D line-segment of charge rather than a single point charge, and that would need to be a thin rod made of an insulator. Because this is a metaball graphics application, I thought a field generator function for...

Good to know. I want to avoid a numeric solution if possible. Yes, the wire could be approximated by straight segments. As the length of each segment approaches zero, I would have some sort of integral, I think.

I have a problem I'm trying to solve for metaball graphics application. I'm going to use an electric field analogy here, but it isn't actually an electric field because the density falloff is ##1/r^s## rather than ##1/r^2##, where ##s## is some arbitrary constant like 3.6 that determines the...

Why? Why do people do this? You never get a satisfactory answer when asking for factual information that normally requires some research or study to find. ChatGPT gives you hallucinations instead. I asked it to give examples of books published by university presses that discuss fringe views...

Welcome. I graduated with a Bachelor's degree in physics, and like you, I was always mediocre in math, but interested enough to maintain a mathematics blog that focuses on empirical math. I'm retired now, and during my career I'd say that beyond algebra, trigonometry turned out to be the most...

I've been there (I'm retired now). I would choose physics. Chemistry is actually physics, when you get right down to it. With a physics degree, you can actually get employment in engineering, as I did. A coworker who actually got his PhD in physics decided he wanted to go into medicine, and now...

We can already make machines that take advantage of a "molecule's always-moving energy". That's thermal energy, and machines that convert heat into other forms of work already exist. A stirling cycle engine does converts heat into mechanical motion, and thermionic generators can convert heat...

Thanks, I believe I figured it out. From the diagram, I have ##x_1^2+y_1^2 = (r+R)^2## where ##R## is the radius of the unknown circle. I also know that ##x_1=a+R## and ##y_1=b-R##. That means ##(a+R)^2 + (b-R)^2=(r+R)^2## and I have a quadratic expression with one unknown, ##R##. That can...

I'm trying to solve this for a model I'm making in OpenSCAD. Given a circle of radius r centered on the origin, and two perpendicular lines at x=a and y=b, where is the center (x1,y1) of a circle that is tangent to both lines and the centered circle? Here's a picture: I thought it would be...

The one that amazed me was Dolly Parton's bluegrass version of Collective Soul's hard rock song "Shine". I'm not a fan of country music, but honestly, it's difficult for me to decide which I like better. Compare them yourself: Collective Soul's original version Dolly Parton's version It helps...

Thanks. I managed to redesign it so the rocker lever moves only 17°. There will be some sliding, perhaps mitigated with a bit of lubrication.

For this project I'm assuming here that the lateral force wouldn't be much different from the lateral forces experienced by the switches under a keyboard, in which the forces aren't perfectly axial to the switch. Yes, you're correct, this is basically a cam. Hopefully the curved pad design on...

The stroke is actually 4 mm, with 2 mm being "dead" and the other 2 mm making electrical contact. With a lever pivot about 8 mm away, that's about 26° but I am not planning for the entire stroke to be used.