Timeline for Simulate the dynamics of a 3D discrete rigid body from "first principles"
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9 at 16:51 | vote | accept | damix911 | ||
| Sep 9 at 16:51 | |||||
| Sep 1 at 0:49 | comment | added | Cort Ammon | @damix911 Stiff systems of equations are notoriously difficult to model numerically. That being said, if you use Hooke's law, with k approaching infinity, you do get rigid body mechanics because for any forces, the displacement of the spring tends to 0. If the displacement of the string is equal to 0 (the limiting case), then you have rigid body mechanics. | |
| Aug 31 at 22:03 | comment | added | damix911 |
By the way, the simulation with springs tends to a rigid body if the Hooke constant is large, but it becomes really tricky numerically. Bear in mind that I am not a physicist, nor an expert in numerical methods, and the simulation that I linked above is very basic, I am sure it can be greatly improved upon. At the same time, conceptually, I wonder if you could create a spring model and apply a limit operation (symbolically, with pen and paper, not numerically) and derive a rigid body model from the spring one by passing the limit k --> +Infinity.
|
|
| Aug 31 at 21:57 | comment | added | damix911 | For instead do something like springs between masses, this is something that definitely I had fun with in the past, and it's very much what inspired me to look into this alternative approach to rigid body dynamics, that I described in this question. I don't quite understand why I can put together something like this (codepen.io/dawken/pen/NWZLLmo?editors=0010) in 10 minutes while I have no clue where to start from if I replace the springs with rigid rods or some sort of massless support (see OP). I presume that I don't know/understand force transmission and generation from velocity. | |
| Aug 31 at 20:31 | comment | added | damix911 | Thank you for the great answer; it sheds some light on a few things that I had thought about but not in much detail. In the past I tried to make some progress by imposing the constraint that the distances between masses never changes; if I remember correctly this implied that the difference between particle velocity is orthogonal to the difference between particle position, for any pair of particles. But I wasn't able to use it to solve for unknowns, back then. Maybe I'll give it another shot. Thanks! | |
| Aug 31 at 4:56 | comment | added | James | Thank you for the helpful information. On a more abstract note, second quantization of QFT is modeled as "springs between masses", does this imply that it is actually modeling an elastic solid? | |
| Aug 31 at 2:50 | comment | added | Cort Ammon | And, just to drop names, the finite element analysis of a liquid or gas is called computational fluid dynamics. Although they don't always use a bunch of masses like this (sometimes it's easier to use volumes instead of masses) | |
| Aug 31 at 2:48 | history | edited | Cort Ammon | CC BY-SA 4.0 |
added 63 characters in body
|
| Aug 31 at 2:48 | comment | added | Cort Ammon | This is actually really important for some relatavistic paradoxes. There are some famous problems, like fitting a ladder in a garage that's too long to fit (if you go fast enough, length contraction lets you fit it in). Paradoxes arise, and many of them are resolved by the fact that in such relatavistic scenarios, we can no longer treat the ladder as a rigid body. We have to recognize that it has some extent and cannot transmit force from one side to the other instantaniously. | |
| Aug 31 at 2:46 | comment | added | Cort Ammon | @James If you have springs between masses, the object is no longer a rigid body at all. It is an elastic body, if I had to give it a name. You can accelerate some masses and it takes a while for that acceleration to propagate to the others. And this model is indeed used to model liquids and gas particles. You would want something less rigid than a collection of springs pre-structured, but the pattern of applying forces through a force transmission element would still apply. | |
| Aug 31 at 2:35 | comment | added | James | Nice answer (+1) I am curious whether modeling using "springs between masses" automatically means that we are modeling a rigid body deep down? Can "springs between masses" be used to model liquid or gas particles where the distances/locations between molecules are not rigid? | |
| Aug 31 at 2:08 | history | answered | Cort Ammon | CC BY-SA 4.0 |