1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding Singular points

  1. Apr 19, 2008 #1

    given the system ml[tex]^{2}[/tex][tex]\theta''[/tex]+b[tex]\theta'[/tex]+mglsin([tex]\theta[/tex])

    how do I find the singular points??

    or any system for that matter - trying the isocline method just not working!! tedious..
    Last edited: Apr 19, 2008
  2. jcsd
  3. Apr 19, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    First that isn't a system, it is a single equation (actually what you wrote isn't even an equation but I assume that was supposed to be "= 0").

    Start by writing it as a system of equations: let [itex]\omega= \theta'[/itex] so that [itex]\theta"= \omega'[/itex] and your one equation becomes two first order equations:
    [itex]ml^2\omega'+ b\omega+ mglsin(\theta)= 0[/itex] and [itex]\theta'= \omega[/itex] or
    [itex]ml^2\omega'= -b\omega- mglsin(\theta)[/itex] and [itex]\theta'= \omega[/itex].

    Now "singular points" (or "equilibrium points), points that are single point solutions to the system, are those [itex](\theta, \omega)[/itex] points where the right hand sides of those equations are 0. (I'm very surprised you didn't know that.)

    In other words, you must solve the pair of equations [itex]b\omega+ mgl sin(\theta)= 0[/itex] and [itex]\omega= 0[/itex]. And that, obviously, reduces to solving [itex]\sin(\theta)= 0[/itex].
  4. Apr 19, 2008 #3
    it is a pendulum system - not sure where the second theta came from in the first term though..

    so it'll be [itex](\theta= 0+k\Pi,w=0)[/itex] where k is an integer

    thank you very much - I have a million and one questions to ask

    the hard part with this one is that I am trying to see it from a phase plane perspective - and visualising where the isoclines converge when you can only draw a couple by hand is tough for a newbie..

    thank you for your time, I will be sure to be back.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding Singular points
  1. Singular points (Replies: 1)