@Erik Mahieu,
If I understand you right. You mean the 1st phase of Trebuchet, can be seperated two (1.1 and 1.2 ) in detail.
http://demonstrations.wolfram.com/TrebuchetBallistics/
phase 1:
1.0 Start from all stationary state
1.1 Only two masses ( counterweight and main beam ) involved in physical with 2 DOF rotation. Becasue, sling or rope at projectile
side is not straight and no force. projectile is still on ground in this phase.
1.2 Three masses ( counterweight, projectile and main beam ) involved in physical with 3 DOF rotation, sling is straight with a
force to pull projectile until it released.
phase 2: the projectile is free throw with ballistic trajectory in air, with air drag. ( Air drag is clear.)
I think below factors in phase 1 might need to consider for efficiency.
mass of main beam as a rigid bar;
damping or friction on three axes;
collision at relearing or after releasing (or the remaining energy of the system, where is it ? ) ;
I think 3rd part of energy is consumed by collision when the beam hit something as end-stop. Usually we can use the position of end-stop to control the velocity direction of projectile. See Siano's page: http://algobeautytreb.com/
It appears Siano uses a bar as end-stop to control the velocity direction of projectile. The moment, when main bean hit on a bar, should be the moment the projectile releasing. Maybe you have conside the 3 part in side equations ?