Torque equilibrium standard equation

[TecHNooB]

J x''(t) + b x'(t) = T(t)

Pretend x is sigma or angular displacement 🙂
J = moment of inertia
b = viscous-friction coefficient
T = torque

Where does b x'(t) come from? I typically see T = J x''(t).

 

[z1ggy]

When i took dynamical systems I don't remember if it was ever explained why it was a first derivative...I just think it comes with it. Its like if you think of an angle..if the angle theta is moving..its now theta prime..or the change in angular movement..aka omega or the velocity. Same thing applies here, however.. I dont know the anti deriv. of friction.

 

[z1ggy]

and to answer where it comes from..if you draw a static diagram ( of lets say a block sliding down a ramp w friction) then you have to include the "b" component relative to your refernece direction. So in this case..the friction is a "+b". Its kind of the same thing as a loaded spring, for a dif. example.

 

[orakle]

Torque due to inertia is dependent on theta'' (alpha/angular acceleration), torque due to viscous friction/damping is dependent on theta' (omega/angular velocity) and "spring" torque is dependent on theta. But if you don't have damping or you don't have springyness, you don't need those terms.