State-Space Model of a Force-Driven Mass

Figure 1.6: Ideal mass $ m$ on frictionless surface driven by force $ f(t)$.

For the simple example of a mass $ m$ driven by external force $ f$ along the $ x$ axis, we have the system of Fig.1.6. We should choose the state variable to be velocity $ v={\dot x}$ so that Newton's $ f=ma$ yields

$\displaystyle \dot{v} \eqsp \frac{1}{m} f.

This is a first-order system (no vector needed). We'll look at a simple vector example below in §1.3.7.

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