A gyroscope-based rotation damper for a motor vehicle, includes a flywheel that is driven via a drive, rotates around an axis of rotation at an angular velocity (ωφ), the flywheel being mounted in a gimbal on the motor vehicle structure by way of a first bearing element and a second bearing element. The flywheel is mounted rotatably around the angle of rotation (φ) at the first bearing element, and the first bearing element is rotatably mounted at the second bearing element around a first angle of rotation (θ) around a first axis aligned orthogonal to the axis of rotation of the flywheel, and the second bearing element is mounted rotatably around a second angle of rotation (ψ) around a second axis aligned orthogonal to the first axis, as well as a controller unit for controlling a shaft drive.