Results 1 to 2 of 2

Math Help - Given a vector field, how does one compute the flow?

  1. #1
    Newbie ajskim's Avatar
    Joined
    Aug 2010
    From
    Philadelphia
    Posts
    13

    Given a vector field, how does one compute the flow?

    Hi,
    I need to be able to know how to compute the flow in R^3 and R^2 given some relatively simple vector fields. My issue is that whenever I read any literature on flows it is very abstract and generalized to the point that I'm not sure what to make of it.
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Basic Idea

    Here is the basic idea.

    let \vec{r}(t)=x(t)\vec{i}+y(t)\vec{j}+z(t)\vec{k} be the position of a particle at time t. Then its velocity is

    \vec{v}(t)=\frac{d}{dt}\vec{r}(t)=\frac{dx}{dt}\ve  c{i}+\frac{dy}{dt}\vec{j}+\frac{dz}{dt}\vec{k}

    If your vector field \vec{F}(x,y,z) is a velocity field then

    \vec{F}(\vec{r}(t))=\frac{dx}{dt}\vec{i}+\frac{dy}  {dt}\vec{j}+\frac{dz}{dt}\vec{k}

    by equating the components of the vectors you will get a system of ODE's that are the flow lines of the vectorfield
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. vector field flow line calculation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 26th 2010, 11:23 AM
  2. Finding flow lines for a given vector field
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 25th 2010, 12:03 AM
  3. Flow Lines of vector Field
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 18th 2009, 09:45 PM
  4. Vector field and flow
    Posted in the Calculus Forum
    Replies: 6
    Last Post: April 28th 2009, 03:32 PM
  5. Finding a flow field
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 13th 2009, 08:44 AM

Search Tags


/mathhelpforum @mathhelpforum