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##

Full Dynamics

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:
.
And state
evolves according to Newton's First Law:

Where
is the vector of external forces applied to the system, and
is the inverse of the system mass matrix. The mass matrix
describes the distribution of mass in the system.

*1999-02-13*