Not to be confused with Dynamics in the context of Physics, although they are similar.

# System Dynamics

A dynamic system is a mathematical description of the relation between an input $u$ and an output y signal. This description is usually given in form of an ODE (Notes From here).

The system has so-called states x. These are variables which allow us to formulate the system behavior in form of a set of first-order ODE for each of this variables.

The standard system description consists of the system dynamics and the output equation. The former describes the timely behavior of the states as a reaction to the inputs and the initial state. The latter describes the relation between the state and the output.

### Related

See how this applies to Vehicle Dynamics.