An endoscope comprises a handle and a shaft with an optical housing at the distal end of the shaft enclosing a camera sensor positioned so that its optical axis is at an angle with respect to a rotational axis of the shaft. The camera sensor is rotatable with the shaft relative to a proximal housing of the handle. A rotation sensor in the handle detects the rotational angle of the camera sensor with respect to the proximal housing. A processor can correct the angular orientation of an image from the image sensor, converting of a rotating variable field of view to a translating variable field of view. A processor can apply variable smoothing of the rotation of the displayed image so that smoothing during rotational deceleration is greater than smoothing during rotational acceleration. The shaft may be enclosed in a trocar that allows for a space between the shaft and trocar that can be used to carry irrigation fluid to or from a space at the end of the shaft.