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Equations of motion for 4 dof

  1. Feb 28, 2016 #1
    Hi all,
    I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed.
    To obtain the equation of motion of this system I started with the method of Lagrange:
    L = T-V.
    With T the kinetic energy: ½mvTv + ½wTIw
    and V the potential energy: mgz
    and this for both the beam and the quadcopter.
    I started with the roll-pitch-yaw rotation matrices (so rotation around the fixed axes) but I do not know how to get the angular speed out of them.
    So my first question is how to find the angular speeds for roll-pitch-yaw angles and my second question is how to obtain the v and the the w in de body frames (that's the easiest for the moment of inertia I think)?Thanks
    upload_2016-2-28_17-35-9.png
     
  2. jcsd
  3. Mar 4, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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