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Implement an implicit differential equation solver #7385

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@calcmogul

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@calcmogul

Now that we have Sleipnir available, we can implement implicit integration schemes. These are helpful for integrating the dynamics of systems derived via Lagrangians, which tend to be messy and hard to solve directly for state derivative.

Here's a resource on implicit integrators:
https://www.astro.princeton.edu/~gk/A403/numinteg.pdf

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