Citation 680 Captain reported diverting after the rudder system jammed. A precautionary landing was made and the rudder worked normally during landing.

Narrative

Approaching rotation speed on takeoff the Pilot Flying said it felt like the rudder pedals locked up in neutral. He rotated the aircraft and we became airborne. Shortly afterward he tried pushing alternately on the left and right rudder pedals and they were indeed immovable. And I found the same thing on my side. I announced that to the Pilot Flying (PF) and we continued a normal climbout and cockpit flow to reach a safe altitude where we could evaluate our status. I engaged the yaw damper; which engaged normally; and then the autopilot and we continued our climbout. The 680 climbs quickly; so we were climbing in the teens as the I pulled out our QRH checklist for Jammed Rudder. We had just flown into ZZZ on a short flight from ZZZ1 at 10;000 ft.; so we knew that cold soak was not a factor. We had not set the flight control gust lock because the winds were calm and we were doing a quick turn. When we started engines; we did a 'full throw' flight control check (including the rudder); per our checklist; so we knew the flight controls were free before taxi. Anyway; as the Jammed Rudder checklist was run with no relief; we [requested priority handling] and diverted into ZZZ2 and used the longest runway; XXL. On about a 3 mile final; the rudder became free; and a normal landing and rollout ensued. Maintenance drove over from our home airport (ZZZ1). Unfortunately the problem could not be duplicated. The aircraft flight control gust lock system was thoroughly inspected and it was determined that it was operating normally and could not have caused the jammed rudder. Maintenance examined the rudder control cables from the rudder pedals to the rudder and found no problems in the flight control system. In short they were unable to definitively identify what caused our jammed rudder condition. Since then the aircraft has flown 4 legs with no further problem.