 Much of the modeling of physical systems takes place in what is called state space, an abstract mathematical space of points where each point represents a possible state of the system. An instantaneous state is taken to be characterized by the instantaneous values of the variables considered crucial for a complete description of the state. One advantage of working in state space is that it often allows us to study useful geometric properties of the trajectories of the target system without knowing the exact solutions to the dynamical equations. When the state of the system is fully characterized by position and momentum variables, the resulting space is often called phase space. A model can be studied in state space by following its trajectory from the initial state to some chosen final state. The evolution equations govern the path—the history of state transitions—of the system in state space. 