Answer is quite simple. They call it a differential because ...
It differentiates !
That means for a unit rev of the tranmission/drive shaft, the average of the revs of the left wheel and the right wheel must be the same.
So: input_rev = (L_rev + R_rev) / 2.
So, in your case, the input_rev was low and the left wheel was stopped (L_rev = 0). This means the other wheel (on concrete) was actually going twice its usual rpm to satisfy its mechanical action. Yes, a brake drag friction level can cause this, but I believe its simply the effect of the tire-on-grass slip friction being low enough so the left side side-gears in the diff. housing locking up. This is how a limited slip diff works. Check the oil level in the diff. Could be low enough for the side gears to be dry but the pinion lube to be ok.
If you jack up the entire rear axle housing, and you spin one wheel clockwise with the input_rev = 0, (engine off, xmission in any gear) then the diff equation says the the other wheel rpms must be -1 (i.e. it turns the other way) to satisfy the differentiator equation.
The differential is there to minimize tire scrub for sharp turns whereby the outer wheel must turn a faster rpm than the inner wheel without scrubbing your lawn, field or wearing the tire tread from scuffing.
It differentiates !
That means for a unit rev of the tranmission/drive shaft, the average of the revs of the left wheel and the right wheel must be the same.
So: input_rev = (L_rev + R_rev) / 2.
So, in your case, the input_rev was low and the left wheel was stopped (L_rev = 0). This means the other wheel (on concrete) was actually going twice its usual rpm to satisfy its mechanical action. Yes, a brake drag friction level can cause this, but I believe its simply the effect of the tire-on-grass slip friction being low enough so the left side side-gears in the diff. housing locking up. This is how a limited slip diff works. Check the oil level in the diff. Could be low enough for the side gears to be dry but the pinion lube to be ok.
If you jack up the entire rear axle housing, and you spin one wheel clockwise with the input_rev = 0, (engine off, xmission in any gear) then the diff equation says the the other wheel rpms must be -1 (i.e. it turns the other way) to satisfy the differentiator equation.
The differential is there to minimize tire scrub for sharp turns whereby the outer wheel must turn a faster rpm than the inner wheel without scrubbing your lawn, field or wearing the tire tread from scuffing.