None of the links or extensive explanations in the posts above answered my original question: "what happens if V2 is significantly exceeded during the second segment? Any mathematical models or real flight tests used to prove it?"
Since people here emphasised (among other things) the best angle of climb for the purpose of obstacle clearance, I narrowed my question down to a more specific one: is there some publication where I can e.g. see a graph or some numbers on how angle of climb depends on speed for a modern jet. That would answer at least in part to my original question.

If it was disscussed here and I missed it, could you please point out to that, so I could see how much climb performance will be lost if instead of climbing at V2+20 any jet of your choice will be climbing at V2+50 during the second segment? I'm interested in numbers, not in "worse" or "somewhat less".

Thanks.