Multibody Systems modeling is a very systematic approach usually results in large sparse Jacbian matrix. I am working to model a system consisting of 11 bodies and 63 constraint equations as soon as i finished the assembly of the system`s Jacobian matrix I got a very ill conditioned matrix even I reviewed the model several times but still have this problem. Later I discovered that it is a common problem using such this method. I am now in mid of my research there is no time to go step back so i tried to deal with this matrix and compared results with other methods there were great differences shown in graphs below Compare Results of MBS modeling with Loop Closure method results. I need an urgent help how to overcome this problem as I said no time to go step backward. I also tried to read about the saparsity there are dozens of research talking about that with a very complicated mathematics far away from my research field. So Any suggestions please to solve this problem.

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    $\begingroup$ It's really difficult to provide anything useful on your question. In essence, you are saying "I tried something, but it doesn't work". But you're not saying what specifically it is you tried, what specifically went wrong, or anything else concrete enough to count as a question. $\endgroup$ – Wolfgang Bangerth Dec 17 '19 at 19:41