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In principle this would be straightforward, but in practice there may be a lot of corner cases to hunt down. The best approach might be a CompoundIntegrator class that lets you switch between a fixed list of Integrators you define in advance. That way we know all Integrators you'll be using at the beginning of the simulation, and they'll all get initialized at the same time.
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SimTK is maintained through Grant R01GM124443 01A1 from the National Institutes of Health (NIH). It was initially developed as part of the Simbios project funded by the NIH as part of the NIH Roadmap for Medical Research, Grant U54 GM072970.