Indeed the systems used for real engine design generally make use of the differential-algebraic equation form in order to have conservation and preserve the rigid body properties. But to do this accurately, you usually arrive at an Index-2 DAE, so you then have to use Pantelides algorithm to do an index reduction before hitting it with an integrator like DASSL. So it takes an order of magnitude of work to hit that extra accuracy and efficiency. But if you don't have Dymola or ModelingToolkit.jl hanging around, this at least decent. Agreed RK4 is a weird thing for people to default to: with almost no work you can at least do better than RK4 at least with Dormand-Price, Tsit5, or SSP methods.
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Indeed the systems used for real engine design generally make use of the differential-algebraic equation form in order to have conservation and preserve the rigid body properties. But to do this accurately, you usually arrive at an Index-2 DAE, so you then have to use Pantelides algorithm to do an index reduction before hitting it with an integrator like DASSL. So it takes an order of magnitude of work to hit that extra accuracy and efficiency. But if you don't have Dymola or ModelingToolkit.jl hanging around, this at least decent. Agreed RK4 is a weird thing for people to default to: with almost no work you can at least do better than RK4 at least with Dormand-Price, Tsit5, or SSP methods.
Would an implicit ODE solver (Euler or higher order) where the constraint solve is included in the implicit step be helpful?