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Phase space trajectory question

  1. Sep 3, 2011 #1
    In my lecture they give the phase space picture for a simple pendulum
    http://mathematicalgarden.files.wordpress.com/2009/03/pendulum-portrait3.png?w=500&h=195

    and then say that adjacent trajectories never diverge and therefore evolution is predictable. I wanted to ask, is the statement that adjacent trajectories never diverge just a consequesnce of the fact that motion of the simple pendulum is predictable, i.e. a small variation in initial conditions will not produce totally different trajectory. Or am I just being stupid and the answer is diferent?
     
  2. jcsd
  3. Sep 3, 2011 #2
    Suppose two phase space paths for the pendulum crossed at a point in phase space. At that point the total energy for the two paths is the same, E = T + V. But if the paths diverge then the total energy can no longer be constant, but the total energy for an ideal pendulum is constant.

    Does that fly for you?
     
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