I saw a project on Hackaday featuring a model rocket with moveable fins to stabilize the rocket's trajectory: Hackaday. The goal was to arc the rocket to a horizontal trajectory and keep it there.
In the comments section, one of the project members proudly states that the rocket used accelerometers only to determine the rocket's attitude: Comment 174820. Other comments on the article opine that without gyroscopes the project goal should have been impossible.
Take the following thought experiment:
If we consider the rocket to begin accelerating along some straight flight path, the accelerometer will measure the acceleration vector to point through the nose of the rocket. Suppose that as the rocket reaches speeds where aerodynamic forces become non-negligible, unbalanced construction or aerodynamic forces cause the rocket to rotate some small angle to a new flight path that balances the forces. There will be some fluttering of the acceleration vector as the rocket experiences aero forces and transitions to the new path, but when it reaches steady state the acceleration vector will again point through the nose of the rocket. No angular difference will be measured. Does this mean that an accelerometer cannot be used to determine orientation of a rocket under power?