Using Lagrangian mechanics, how would I go about trying to model the double inverted pendulum that can swing out of plane.

A lot of existing work has been done on the planar double inverted pendulum. However I am trying to model a double that can be able to swing out-of-plane due to an actuation torque created on one end of the double pendulum as it swings.

There already exists a robot that can brachiate along a planar line, like how a monkey would swing from branch to branch. I am trying to introduce out-of-plane motion such that the robot can be able to swing onto a line parallel to its current position.


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  • $\begingroup$ The method of writing down the Lagrangian, and deriving the Euler-Lagrange equations, is basically the same (this is one of the strengths of Lagrangian mechanics). Where exactly are you having trouble? $\endgroup$ – Arthur Aug 13 at 14:16
  • $\begingroup$ I see, and definitely agree. However, with out-of-plane motion, I am adding additional dynamics to the system. I want to be able to actuate the one end of the pendulum so that its motion becomes non-planar. Essentially I am asking how this additional dynamics will affect the existing equations. $\endgroup$ – Sizwe Lekoba Aug 13 at 14:30

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