This morning (in 30deg F weather), I had a very mild version of this occur 2 times, each before the car had warmed up (within 5 minutes of starting). Both of these instances occured as I was slowing down approaching a red light. Here were my conditions:

* Traveling 20 MPH as red light appears.
* ICE is running at cold-idle speed (probably around 1000 RPM).
* Breaks are gently pressed to slow vehicle as red light nears.
* As speed decreases below 10MPH, ICE appears to be put under a load, RPM appears to decrease, and ICE starts to shake progressively worse (though not severe) until vehicle stops.
* Once stopped, RPM goes back to around 1000 and ICE is smooth.

From what I could deduce, the power split device seemed to allow the ICE RPM to drop too low as the vehicle slowed down, thus causing the ICE to approach (but not reach) a stall point. I believe that the violent shake mentioned in this post is a more severe form of this, where the engine actually REACHES the stall point, but the power split device doesn't let it stop like a normal ICE would.

If this is confusing, picture an engine connected to a hand crank. A person can turn the crank and cause the engine to rotate. Assume a minimum RPM of 800 before the engine would stall under its own power. Now, picture the person turning the crank at a constant 400 RPM, but with no fuel going to the engine. Fuel is then supplied to the engine, causing it to fire. The person is strong and prevents the engine RPM from going above or below 400 RPM. At this RPM, severe misfiring is occurring, causing the engine to shake severely, but not stall because of the person controlling the hand crank.