Sheet 03.2 — fig. 02

Trebuchator

Counterweight siege engine calculator

Three counterweight topologies — hinged, bolted and floating arm — are solved by one Lagrangian assembler, so they are the same physics rather than three approximations. A shot runs in three stages: dragged along the trough under a holonomic constraint, swinging free on the sling, then flying under quadratic drag with wind.

Liftoff is not a tuned threshold. The Lagrange multiplier on the trough constraint is the normal force, and the instant it passes through zero falls out of the solve. Beyond range it reports peak sling tension, peak frame reaction and beam bending moment at the pivot — the numbers you need to size an axle rather than guess one.