Dissipative force

A dissipative force is a force for which the energy of the system is reduced when the force takes place. The energy is transferred outside of the system and typically transformed in a different form of energy, the most common type being heat. Common examples are friction and viscosity. Forces that are not dissipative are said to be conservative.

A simple model for a generic dissipative force is

where $\mathbf{v}$ is the velocity of the object moving, $c>0$ is a parameter that determines the intensity of the dissipation and $n$ is a positive integer. $c$ may be a constant or may vary in both space (e.g. in an heterogeneous medium) or in time. This model also includes the assumption that the force's direction is opposite to that of motion, so equal to that of $-\mathbf{v}$.