In America such calculations are normally done with decade boxes and variable voltage power supplies.
There are simply no end of circuits already solved -- sitting on the shelf for this and that purpose.
You need to hit the books -- at a library dedicated to electrical engineering.
You'll also find amazing amounts of knowledge in basic electrical engineering texts.
As for the principle I think you'll agreed it's obvious: a steady DC induced magnetic field in the MAIN WINDINGS will cause the rotor - -with its induced magnetism to brake to a stop.
One need only figure out how to break the AC connection ( a switch ? ) while making a DC connection. ( the same switch ? )
A decade box ( of resistors ) tapping a DC power supply ( half-wave ) ) would start out at high values and low current -- later being adjusted down to a value that stops rotation without collateral damage...
This test rig would then be followed by a production solution with tweaks for switches and time delay before drop out.
----
However, it does seem over engineered since a simple pause in power would seem to bring a washing machine to an acceptable halt without further complication -- and it's expense.
======
More generally, we are electricians who install field wiring/ wire buildings.
As a rule, we don't have bench equipment and are entirely unconcerned about solving engineering problems -- particularly ones that constitute the typical college course.
I'm sure that you'll find other forums much more dedicated to such topics.
They're out there.
It really is a different mind-set.
We tend to be focused on what's going to make our customers and inspectors happy.
We're not allowed to self-engineer -- when it's going into a building.
That's the motivation for the NEC. Only tested and proven devices are deemed worthy - -and only when they've been installed according to manufacturer's instructions.
That turns out to be a lot tougher than one might think. Just that alone can take 10,000 hours of field experience on top of 1,000s of hours of book learning.
Cheers.