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## Main Question or Discussion Point

Lately when doing a simulation for a quadrocopters most reports I've come across regarding modeling use Eulers equation of motion. That makes sense, as the quadrocopter is a body rotating in 3 dimensions.

Then I tried to model the system using Lagrange equations instead but I don't get the same result. I wrote the Lagrangian as

L = T-U = T = 0.5*(I

But applying Lagrange equations to L doesn't give Eulers equation of motions. Actually though, it gives the linearized version of Eulers, when linearized around the angular velocities zero.

Why is this? I must have missed some crucial condition that must be fulfiled for Lagrange equations to hold true? Did I get the expression for the lagrangian L wrong? Is it because Eulers model a continous mass distribution, while Newton/Lagrange rather deal with a system of masses? I assumed the lagrangian to be in the rotating frame, as are Eulers equations in their standard version.

Then I tried to model the system using Lagrange equations instead but I don't get the same result. I wrote the Lagrangian as

L = T-U = T = 0.5*(I

_{x}ω_{x}^{2}+I_{y}ω_{y}^{2}+I_{z}ω_{z}^{2})But applying Lagrange equations to L doesn't give Eulers equation of motions. Actually though, it gives the linearized version of Eulers, when linearized around the angular velocities zero.

Why is this? I must have missed some crucial condition that must be fulfiled for Lagrange equations to hold true? Did I get the expression for the lagrangian L wrong? Is it because Eulers model a continous mass distribution, while Newton/Lagrange rather deal with a system of masses? I assumed the lagrangian to be in the rotating frame, as are Eulers equations in their standard version.