mathematical model of vdrift cars

[joevenzon]

Here's how everything is connected together:

engine --- crankshaft --- clutch --- transmission --- driveshaft --- wheels

The engine is simulated as a rotating body with inertia and the wheels are simulated as rotating bodies with inertia. The crankshaft is always spinning at the same speed as the engine, and the driveshaft is always spinning at the same speed as the wheels. Let's also assume that the transmission is in a forward gear that has a 1:1 ratio, so we can ignore it.

But if the clutch torque gets bigger than the crankshaft torque or lets say we have no crankshaft torque at all (throttle = 0), the torque is set to -max. clutch torque and hence car accelerates anyway ( because of two negative signs ).

Correct me if I misunderstand your statement, but you're saying that the engine is at idle but the wheels are rotating like the car is moving backward, right? Let's assume that we had the clutch disengaged and then we rapidly engage it. In that case, the torque at the crankshaft from the engine is zero, the torque at the driveshaft from the wheels is negative, so the clutch causes the wheels to get positive torque and the engine to get negative torque, which pushes the car forward a little and slows the engine (probably killing the engine). This makes sense if you think about it.