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Lydia's recommendation, which is supported by the "Discovering Modern C++" book that I've been reading, is to use an existing numerical integration library like Boost.odeint. Thus this might just be a wrapper around Boost's implementation of Euler integration.
Resolved by 1c8cc3a. Dealing with interactions between Eigen and ODEInt is a bit of a struggle, so any ODE integration wrapper that is implemented should abstract away ODEInt details like this wrapper does.
This is a basic physics simulation technique, but it's also a necessary component of testing PARL.
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