What are the collision forces applied to the stops in a moving triple pendulum?

Sep 2018

it's been a while since I did not use lagrangian mechanics and all this stuff and would bet it's needed for my purpose.

Introduction : if I take a simple pendulum and make it collide on its origin with a stop, how much will suffer the stop ? Knowing that the pendulum is subject to an actuating torque + gravity + its current acceleration. (let's say that all the mass is on the extremity and that the link is l meter long.)

I guess we can agree that momentum applied onto the stop = torque + l*(g perpendicular part(t) + m* perpendicular acceleration(t) part).

Actual problem : what if I take now a triple pendulum and want to spawn an instantaneous stop onto its origin, while there are 3 torques + 3 gravity forces + 3 accelerations... but also some joint reactions, right?
Or the same with only a double pendulum...

So assume we know both velocity and acceleration at each mass (we can work with either cartesian or in d²(q_i)/dt²)... What is unclear on my figures is that unknown joint reaction should also appear on the mouvement drawing (the first one).

Triangle obstacles spawn from nowhere but are fixed and can provide an infinite reaction intensity if needed.

So first I wanna stop the first link, but then I don't know how to determine how much are involved the unknown joint reactions at A2 and A3...

In a nutshell, at the time t3 what is the TOTAL torque applied on A1, assuming forces that appeared at t1 and t2 are still pushing ?
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