There are a wide variety of ways to model physical systems. The model needs to include parameters that describe the links that compose the system, as well as information about the hard constraints that connect these links to one another. A model that only includes this information is called a kinematic model, and can only describe the static states of a system. The state vector of a kinematic model consists of the model state, .
A system in motion is more completely modeled when the dynamics of
the system are modeled as well. A dynamic model describes the state
evolution of the system over time. In a dynamic model the state vector
includes velocity as well as position:
evolves according to Newton's First Law: