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Unconstrained multibody dynamics

Hello everyone, 

 

I am currently working on a bar-linkage simulation and decided to use multibody dynamics to try to perform this analysis. So basically everything seems simple and clear for examples such as double-pendulums or 4-bar linkages. And i obtain the lagrangian equations or hamiltonian without too much problems. However, I would like to model bar-linkage (actually for a start just a bar chain without any ramifications) that is not constrained. By this, I mean that the bar is not attached to any support. For example a bar is in free-fall. I think in this case the system of equations would be singular.

I don't really see how to handle this problem. I thought of constraining the center of mass to an imaginary frame but the center of mass is actually always moving in regard to the whole system.

If anyone got any thoughts about this problem, your help would be greatly appreciated ;).

 

Best regards and thanks in advance for your help.

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