When you apply a force to the handle, assuming the rear wheel is always aligned to its direction, you can consider the longitudinal component and the lateral component separately. The lateral component adds a torque which causes a rotation around the mid point between the forward wheels. The longitudinal component makes the jack advance or backup.
F_long = F * cos(alpha)
F_lat = F * sin(alpha)
where alpha is the angle you are turning the handle.
At 90 degrees, there is no longitudinal component as cos(alpha) = 0, but sin(alpha) = 1 so it is pure torque and the jack should indeed spin in place.
Assuming the handle is applied to the center of the rear wheel and the distance between the axle of the rear wheel and the midpoint between the front wheels is L, then the rotational torque is:
T = F * sin(alpha) * L
With the forces and torque known, assuming you know mass and moment of inertia around the Z (pointing up) axis, you can calculate the accelerations, then integrate to determine the velocities and integrate once more to determine position and angle of your jack.