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Ropewalk equations

  1. Nov 20, 2004 #1
    Hi,
    I am trying to do a model for a ropewalk.
    I would like to describe it with two first order differential equations. If we consider a person walking on a rope there are two quantities changing; the speed of a rope in horizontal direction and the angle of a person. I have to write this in a correct mathematical form. Any advice would be helpful.
    Regards,
    Niko
     
  2. jcsd
  3. Nov 21, 2004 #2
    If we think about the relations between quantities:
    Let's look an angle between vertical line and the man on the rope and we assume equilibrium at x=0.
    A=angle, v=speed on x direction, k and g are some coefficients
    dA(t)/dt=k*A(t)-g*v(t)
    My explanation:
    If the angle is greater, the angle is changing faster and if the speed in x direction is greater, the angle is changing slower thus I put -.
    If I try to write an equation for dv(t)/dt I have some problems:
    dv(t)/dt=h*A(t)-g*v(t)
    Explanation:
    If the angle is greater we have to accelerate faster to gain balance and if the speed is greater we have to accelerate slower, because we already have some speed. But the problem is that the right sides of equations are same, so I'm not sure about my illustrations.
     
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