The nacelles move because of the variable warp geometry. It was a way to get around the subspace damage that conventional warp drive causes. The nacelles shift position while the ship is at warp, they need to contstantly move in order to adjust to changing spacial and subspace conditions
It was later found that the variable warp geometry could be achieved with fixed naceles such as on the Enterprise E
Is there on screen canon to support this?
No, unfortunately there was no screen canon to support this. It is widely accepted fanon