In the following rotational mechanical system, there is a driving torque (T(t)) exerted on disk (J_{1}) and

Question:

In the following rotational mechanical system, there is a driving torque \(T(t)\) exerted on disk \(J_{1}\) and a load torque \(T_{L}(t)\) exerted on disk \(J_{2}\) (Figure 2.54).

(a) Draw the free-body diagrams for the system.

(b) Choose the minimum number of state variables for this system and give a rationale for the choice.

(c) Express the dynamic equations in State-Variable Matrix model (i.e. obtain \(A, B, C, D\) ) where both the applied torque \(T(t)\) and the load torque \(T_{L}(t)\) are considered as inputs. The output is the torque in the shaft \(k\).

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