# Determine position given linear and angular accelerations

 P: 2 Hello, I would like to know how to calculate (x,y,z) in the inertial frame at any given time, t for a body I am testing. On the body, I have one instrument that can give me (u,v,w) in the body frame, another instrument to give (roll, pitch, yaw) in the body frame, and yet another instrument that can give both linear and angular accelerations (again in the body frame). I am sampling at 100 Hz, but I want to determine position in the inertial frame from t=0 until the end of the test spot. I am assuming at t = 0 that the body is starting from the origin (0,0,0). At each new time step (i.e. t = t0 + 0.01) I get another data packet containing the information listed above. Currently, we do a very crude method for determining position by integrating the linear velocity vector over the time step, but I'd like to improve upon this by starting with the linear and angular acceleration vector and integrate to get position. Any help is greatly appreciated, thanks!
 P: 2 While continuing to try to solve this problem, I was wondering instead if I should use my velocity and rotation relative to the body frame (u, v, w) and (roll, pitch, yaw) and translate the velocity frame back to the inertial frame using the Euler (3-2-1) direct cosine matrix? Is this approach valid? If I apply the 3-2-1 direct cosine matrix, and multiple that by my velocity vector, doesn't this put my body velocity vector into the inertial frame?

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