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Here's my problem. I have an initial orientation and angular velocity of a body and a final orientation and velocity occurring at a specified time in the future. I have control over how input formatted; I'm assuming I'll have quaternions. I need to determine whether or not it's possible for the body to rotated between those states given constraints on angular velocity and acceleration in the body frame. Does anyone know of an easy way to do this? I was thinking of formulating it as a constraint optimization problem with variables representing orientation at each of a number of time steps, but I think that might be too slow. I'd really like to be able to solve this problem about 10 times per second, and I'd appreciate any input on an approach to doing so.

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