Recently I watched The Martian and the space vehicle Hermes in the movie had a rotating platform. I wonder if that would significantly cause the vehicle to be inclined in direction? Does a spinning platform/living space on a space vehicle, used to provide artificial gravity, create momentum that inclines the trajectory of that vehicle?
The trajectory however is independent of orientation. You could change the velocity of your spacecraft (speed and direction) without changing the orientation (angle relative to the universe). This could be done with multiple rocket engines firing at different amplitudes to get the desired thrust vector or with a rocket engine that could be re-positioned about the crafts center of gravity.
If changing the orientation of the craft is important for engine positioning, solar, or other; 2 living spaces could be used rotating in opposite directions. The gyroscopic force would still put a large load on bearings however, but slow changes in orientation would be fine.
Another option would be to have large control gyroscopes that have rotational inertia at the same order of magnitude as the rotating living space. These could be rotated to counteract the living space angular momentum and control the angle of the craft.