= State vector
A <state vector> collects variables sufficient to specify an instantaneous state for the chosen evolution rule. For a mass on a spring, $(x,v)$ is a state vector, whereas <position> alone is generally insufficient. The second-order equation $m\ddot x+kx=0$ becomes the first-order system $\dot x=v$, $\dot v=-kx/m$.
Its entries can have different units: <position> and <velocity> need not be added or compared without a defined scale. More complicated material models can also require internal variables that record loading history. Two samples with the same measured extension can have different internal states and different subsequent responses. A useful state vector therefore follows the model's physical memory, rather than simply listing whichever observables are easiest to measure. Its evolution traces an <orbit> in the associated <state space>.
Back to article page
