Cineversity

I’m experimenting with pendulums and trying to model one that is physically accurate but having some trouble getting the math to work out. Attached is my test scene.

I am using the formula here: https://en.wikipedia.org/wiki/Pendulum

The centers of the support and bob are 1500cm apart and the starting angle is 45 degrees. The animation frame rate is 30 fps. And in the project settings I have set gravity to 980.67 cm/second-squared. IN the Rigid Body tag on the bob I have set both linear and angular damping to 0.

The math for the period is: 2*pie*sqrt(1500/980.67) * 30 fps = 233.1 frames… (Happy to have my math checked).

I end up seeing a period of about 244 frames or so…

I would appreciate insight into how I might be thinking about things incorrectly, other parameters or constants to tweak, use of the Connector object, etc.

Thanks,
Greg

Hi Greg,

There are specific parameters in the default settings that reduce energy. If you like to use an idealized formula (nothing wrong with that, but it would work only in a vacuum), then you need to take those out of the equation (i.e., set it to zero). Linear and Angular Dampening are the primary energy ‘Eater” here.

Typically entropy sets in, and that little bit of air will stop the motion at one point.

Any simulation in 3D/CG applications is not (!) targeting physical accuracy, and yes, people love to throw those words around.
It is physically plausible and tends to get as close as possible to reality. This is done to keep the calculation times short, especially in GI, where light is also just on the level of plausible.

An accurate pendulum formula would have earth movement, air temperature, and surface roughness of the “bob”, etc., in it. Furthermore, Gravity is not a fixed value; it depends on where you are, simplified, the more you get away from the center, the smaller the number is. Even the moon has influence.
https://en.wikipedia.org/wiki/Gravity_of_Earth

I list this as all of those could be considered valuable to get precise results. But shorter formulas are used, like yours, to keep it manageable. The same is true for the “Bullet Engine”.

I think the setup comes close. If you need it timed, export it as Alembic and retime the import.
Two version with different degrees
https://www.dropbox.com/s/lylnfvoj64l7gi9/CV3_2023_drs_22_DYpe_01.c4d.zip?dl=0
https://www.dropbox.com/s/9b8m6y5itzj62sf/CV3_2023_drs_22_DYpe_02.c4d.zip?dl=0

All the best

I discovered my error. I was starting at 45 degrees and the simple formula I used was for angles << 1 radian. I had assumed that 45 degrees was smaller enough than 1 rad. However, that’s not the case. In reading further the simplified formula works for very small angles, single digit values.

When I use the exact formula I get a value of 242.4 frames. Looking at the simulation again and testing with 242 frames the motion is almost perfect!!

BTW, I had taken into account the items you mention above, damping, etc. And noted that since this simulation is unaffected by air, variations in gravity, the moon, etc., it should be perfect within rounding error. And, as my recalculation shows this is indeed the case.

The reason that I am investigating this issue is because I have seen so many animations where the motion should be governed by physics yet the motion is subtlety but noticeably incorrect. Evoking in me something similar to the ‘Uncanny Valley’ effect, especially at the two peaks of movement. I assume these animations are likely driven by key-framing and getting the ease in/out to match physics would be difficult (I know I have tried).

In any case I am happy with the movement at this point.

Thanks for your insights!!

Greg

Thanks a lot, Greg, for the detailed reply.

Your reply is very much along my idea: One can only simulate what was understood already in detail. Your exploration will pay off many times over.

Yes, studying reference material often helps to animate correctly. I can only encourage you to have a camera and capture things like that, then use it as background to animate. We all have some memory about things, but they often get simplified. Reference material or formulas help in such cases a lot. I think you are doing it very well.

My best wishes

** I can only encourage you to have a camera and capture things like that, then use it as background to animate. **

Very good suggestion. Thanks.
G

Thank you, Greg, for being so openminded.

Have a great weekend

Here are two links to the results of my investigation into pendulums.

https://www.flickr.com/photos/8395936@N03/52363264828/in/album-72177720298418819/

https://www.flickr.com/photos/8395936@N03/52372501625/in/album-72177720298418819/

Thanks for your help Dr. Sassi!

Greg

Thank you very much, Greg, for sharing these!

Beautiful work and so motivational!

It is a pleasure to see how you translated our technical discussion into something so aesthetical.

My best wishes