06 - The simplest way to simulate a triple pendulum

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06 - The simplest way to simulate a triple pendulum

Рет қаралды 14,592

Күн бұрын

For the source html code and all other tutorials see matthias-research.github.io/p...
In this tutorial I explain how to simulate hard distance constraints stably. They can be used to simulate cloth, ropes, hair, robots or sand.

Пікірлер: 31

@AJWeeks 2 жыл бұрын

Great explanation :) There is a small typo in the equation at 2:37 though, weights should be divided by w1+ w2, not w1 + w1.

@7steelrainbow 2 жыл бұрын

Thank you for this great tutorial. Seeing that match of the trajectory with the analytic method is amazing.

@novidtoshow Жыл бұрын

I think it would be good to plot the total energy of the system in time. This would help us understand whether the solution is dissipative or not.

@samsara2024 4 ай бұрын

I am loosing energy, even with a single pendulum what could be the reason?

@novidtoshow 4 ай бұрын

@@samsara2024 Your time integration is not conservative. The numerical discretisation is "leaking" energy. Use a 4th-order Runge-Kutta or a time-implicit method like backwards-Euler.

@konstantinbondarenko5235 Жыл бұрын

Thank you for this great tutorial.

@dalegriffiths3628 Жыл бұрын

Super cool video, got it working great in python too - thanks very much.

@EastingAndNorthing 2 жыл бұрын

You are my lord and saviour Matthias!!!

@TenMinutePhysics 2 жыл бұрын

May the physics be with you ;-)

@mingshey Жыл бұрын

I've recently started simulating double and triple pendula. I use Maxima to generate the necessary ODEs from the Lagrangian and then feed them to the rk(RK4 iterator) function. That way I can avoid coding the haywire ODE directly. I check the mechanical energy drift to see if the calculation is dissipative.

@shulehr Жыл бұрын

i think video would reach wider audience if there was something about constraints and rope/cloth in the title. Most people aren't interested particularly in pendula

@BlaseAnDerHand Жыл бұрын

Merci, guets tutorial.

@santiagozera Жыл бұрын

Awesome!

@leoli440 11 ай бұрын

wonderful :)

@AdityaChaudhary-oo7pr Жыл бұрын

Thanks !! subscribed

@landsgevaer 9 ай бұрын

You should be able to estimate the error by solving with two different step sizes. That works for any number of links.

@santiagozera Жыл бұрын

This is beautiful. Are there any books to learn this stuff? Could you enumerate some, please? Thanks in advance

@herseem Жыл бұрын

This is fascinating. I've written a 2D gas flow simulator which was relatively easy, and it exhibits patterns you'd see if you were watching water flowing flowing through a similar shape where the height of the water is analogous to the pressure of the gas at any given point. One thing interests me greatly though: From the path of the end point, what method would you use for working out the structure of the pendulum? ie, how many links and which weights? I have a reason for wanting to know how to do that. It's essentially reverse engineering a chaotic pattern which of course has multiple applications, preferably without doing a brute force method.

@adelelopez1246 2 жыл бұрын

Is there a simple way to make sure energy is conserved, even with less steps?

@TenMinutePhysics 2 жыл бұрын

You can measure the energy loss and add it evenly to the particles. However, objects are typically highly damped so instead of pumping energy into the system, extra damping terms are added to the equations in general.

@Zymplectic 2 жыл бұрын

@@TenMinutePhysics That's not a good advice. Compensating energy errors by arbitrarily modifying the energy will generate errors - it is not symplectic, it is not time reversible and it will not exhibit a correct behavior in phase space. Masking numerical errors with damping effects is not really an option if your system is supposed to be energy-preserving To conserve energy with less time steps, you'll obviously want to use higher order symplectic integrators.

@TenMinutePhysics 2 жыл бұрын

@@Zymplectic Yes, that is not really physically correct. Some people have done it in graphics. However, as I said, the real strength of PBD is not energy conservation but robust handling of zero-compliance constraints and simplicity. In the real world, nearly energy conserving systems are rare. In contrast, most objects are highly damped which is the reason why additional damping terms are used significantly higher than the numerical damping introduced by implicit integrators. In contrast, stretchy cloth looks really bad - if not intended :-)

@Zymplectic 2 жыл бұрын

@@TenMinutePhysics It wasn't a critique of the video which is on point, but merely to the "out of context"-point of arbitrarily adding energy to compensate for dissipative numerical errors. The real world being "inaccurate" does not prevent us from making accurate energy-preserving simulations though. I'd agree that energy conservation is typically not what you want for cloth simulations. Unless the cloth is floating in space...

@samsara2024 4 ай бұрын

I made the same algorithm using c#. It works but I can see a global dumping of the energy even with a single pendulum. What could be the reason? Thanks!

@ghostbusterz 5 ай бұрын

In code you subtract the actual distance *from* the rest distance (L0 - L), but in the mathematical equation you show subtracting the rest distance *from* the actual distance (L - L0). This is quite confusing.

@SellusionStar Жыл бұрын

When I first implemented a double pendulum (using analytical equations) I thought I'm "stimulating" it. But that wasn't true of course. At least if we don't consider the integration part. I then tested Euler method vs RK4, to see which is more stable. It would be interesting to see which is faster (amount of operations vs. substeps)

@BooBaddyBig 8 ай бұрын

Your hard constraint of position method does not conserve angular momentum. You should adjust the tangential velocities as you move the particles.

@ai_serf Жыл бұрын

Damn... So, there's no analytic solution to the derivative of a 2 pendulum problem. I feel sad when I see you're sim diverge from the analytic path. I wish we could simulate reality a bit more accurately for personal reasons. I understand for games and practical applications, the accuracy is good enough with numerical methods.