> I hope you will provide explanations on why no one has been able to obtain the synchronization using SimMechanics or with an algebraic loop.

Synchronisation cannot happen in a linear framework, that is a long known fact from electrical oscillators. Coupling them leads to several modes with slightly different resonance frequencies (”off tune”), and increasing the coupling separates the frequencies further.

So the key is nonlinearity. My guess is that it is the driving force, but I did not study other options.

How you model it should have no influence: SimMechanics, SimScape or plain Simulink, they all show the same behaviour.

That was a good challenge.

At first I thought this challenge was going to be easy, I assembled a SimMechanics model, clicked play… but the pendulums are not synchronizing, as mentioned by Parasar in his post.

Then I thought, let’s try with Simulink. I implemented in a vector form the equations provided and then face two choices:

- By default, the coupling of the equations results in an algebraic loop. I never like to have an algebraic loop in a model, but tried to let the solver resolving the algebraic loop. The results are similar to the ones from Simemchanics. It looks like the Simulink algebraic loop solver is doing a job similar to the SimMechanics solver. I cannot explain the exact reason, but my guess is that the algebraic loop solver removes the non-linearity that makes the pendulums synchronize in real life.

- My standard way to remove algebraic loops is to introduce a delay in the feedback path. In that case, the pendulums synchronize but the model becomes instable. The maximum sample time of the Simulink solver must be adjusted to an appropriate value to obtain an acceptable tradeoff between synchronization and stability.

I implemented the model using a vector approach. It allows easily changing the number of pendulums and modifying the algorithm.

I hope you will provide explanations on why no one has been able to obtain the synchronization using SimMechanics or with an algebraic loop.

Guy