Help with pendulum animation.

I'm not sure that it's exactly a pendulum. I basically need to animate a necklace that has 6 links connected by an "invisible string". I need the animation to work as the necklace is turned.

As if the person wearing it were doing a cartwheel.

I'm attaching an rough sketch of what i'm talking about.

I just need an algorithm to animate this. I'm not very good with physics and could really use some help. I don't have access to any physics libraries or simulators so I'll actually need to code the whole algorithm.

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