2DoF dynamics of a carousel (rotational pendulum): Euler-Lagrange equations

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 19:50

Summary:

This video discusses how to model a merry-go-round (well, really with just one element hanging the mechanism is often called a “rotational pendulum”) using the Euler-Lagrange formalism.

The first ten minutes review the kinematics (defining the coordinates that describe the motion plus deriving expressions of positions, speeds and accelerations of the elements of the system based on said coordinates). The jacobian command is widely used to apply the “chain rule”. If the manipulations are unfamiliar to you, perhaps you should preview the video [derivsmlEN].

Next, the Euler Lagrange equations are expressed with the Symbolic toolbox and the meaning of the different terms is analyzed, grouping them in the usual way $M(q)\ddot{q}=\tau +C(q,\dot{q})\dot{q}+G(q)$, i.e., with mass matrix and Coriolis terms.

Matlab code for simulations will be discussed in next video [tiovELsimEN], and further digression on particular cases of interest will be discussed in video [tiovEL2EN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.