How Do Dissipative and Conservative Systems Differ in Dynamics?

[broegger]

Hi.

I'm reading a book on deterministic chaos, and an important distinction seems to be the one between dissipative and conservative dynamical systems. A dissipative system is defined as a system whose "phase space volumes shrink", whereas in a conservative system phase space volumes are conserved.

What does this mean?

 

[Astronuc]

Nice discussion of Phase Space
http://en.wikipedia.org/wiki/Phase_space

In mathematics and physics, phase space is the space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. A plot of position and momentum variables as a function of time is sometimes called a phase diagram.

In a conservative system, momentum (velocity) is conserved, i.e. not dissipated (reduced), and a particular set (domain) of position and momentum (velocity) statepoints remains. In SHM, e.g. pendulum, the velocity and position have a preserved relationship.

In a dissipative system, the momentum (velocity) is continually decreasing as a function of position/displacement, as energy is lost (dissipated) with continued motion, until the magnitude of velocity (speed) reaches zero as kinetic energy reaches zero.