Thread: Limited Slip Diff

Can Someone explain to me how exactly a limited Slip Diff works.
Here is the senario.
I'm in 2 wheel drive [ surf] and I go over a slight rise on such an angle where the two front wheels are on the road, the left hand back wheel is firmly on the ground [ the front of the truck is facing down slightly] but the rear right wheel is supended in mid air.
I go nowhere.
The rear left wheel just spins.
Now I thought a LSD was supposed to send the power to the wheel with the most grip,to enable you to get out of situation such as this, which it didn't .So what it the point?
Am I missing something here.
I know I have an LSD because it is written on the diff.