I ran the numbers for Spinlaunch's actual system. This is left as an exercise for the student. What you need to know is it's at a 45m arm, it weighs 11,200 kg, it's 25 feet long and prolly 3-4 feet in diameter. It's "suicidal urge" is gobsmacking.
And again. Those aren't real numbers. But there AREN'T ANY REAL NUMBERS AROUND SPINLAUNCH. In order to get to that math you're spinning a pair of orcas around a 45m circle at 450 rpm and then flinging them into the air at Mach 6. I mean, c'mon. Presume you build this thing out of rainbows and hope, dumb-ass dynamics is still slapping you down. A half-gram USB-C connector under 10,000g weighs this:
Design for that. Go ahead. Design for it in not one axis, not two axes, but the transition between those two axes. Also tell me you're going to aerodynamically stabilize a two-body problem with this thing.
I don't know what kinda yaw is recoverable at transsonic speeds but I'll bet those are heroic calculations, too.
And it kinda feels like this is more math than has ever been done around Spinlaunch.