Results 1 to 2 of 2

Math Help - Phase Space/ State Space/ Phase Portrait

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    50

    Phase Space/ State Space/ Phase Portrait

    I am having difficulty understanding the concepts of phase space, state space and phase portraits.

    From what I've seen, a phase space is a vector field representing the behavior of points in a dynamical system.

    A phase portrait is a set of curves in a phase space corresponding with a given initial condition.

    I'm not sure what a state space is but it seems similar, if not the same, to phase space.

    An example is given that \frac{dx}{dt}=\sin{x}. And I am given this graph corresponding to this equation.



    Would this be a graph of the phase space? What would the phase portrait look like then? I'm pretty lost on how to construct a phase space/ phase portrait.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280
    According to this definition
    Phase space - Wikipedia, the free encyclopedia
    "In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901[1], is a 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."
    In your graph not all possible states are shown but a curve with some initial conditions.

    I think that your graph a phase portrait.
    The definition of phase portrait is here
    Phase portrait - Wikipedia, the free encyclopedia
    Last edited by zzzoak; October 12th 2010 at 01:57 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trajectories in phase space
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: April 15th 2010, 03:06 PM
  2. Phase Portrait using Isoclines?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 23rd 2010, 01:43 PM
  3. state space help
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: January 13th 2010, 01:23 PM
  4. state-space model
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 14th 2009, 07:42 AM
  5. phase portrait for ODE
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 7th 2007, 07:04 AM

Search Tags


/mathhelpforum @mathhelpforum