A state variable is a coordinate used to describe the instantaneous condition of a dynamical system sufficiently completely to determine its future evolution under a specified model and input. For a simple pendulum, its angle and angular velocity form a state; angle alone generally does not, because the same position can be traversed in either direction.
A second-order ordinary differential equation becomes a first-order system by setting : and . The choice of state variables therefore reflects the memory required by the model, and differs from merely listing measured outputs.
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A state variable is a quantity used in the mathematical modeling of dynamic systems to describe the system's current state. State variables represent the essential information needed to predict the future behavior of the system based on its present conditions. They encapsulate the system's memory, meaning that knowing the values of the state variables at a given point in time is sufficient to determine the future evolution of the system.