Double Pendulum (One pendulum hanging from the other)

[CAF123]

This makes sense, the energy has to go somewhere so it appears in the potential term. But in both defintions of x1 and x2, the kinetic energy is decoupled (or at least decoupled after neglection of small elements) while the potential is only decoupled in one definition. Is there a reason for this?

 

[voko]

I think you are mistaken. If x2 is defined as it was originally, the horizontal displacement from the upper mass, then kinetic energy is not decoupled, you have a product of x1 and x2's derivatives, and the kinetic energy matrix has non-zero non-diagonal elements.

 

[CAF123]

I think you are mistaken. If x2 is defined as it was originally, the horizontal displacement from the upper mass, then kinetic energy is not decoupled, you have a product of x1 and x2's derivatives, and the kinetic energy matrix has non-zero non-diagonal elements.

Indeed I was mistaken. Thanks voko, you have been a big help!