Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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: ½mv^{T}v + ½w^{T}Iw

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

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# Equations of motion for 4 dof

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