Rigid bodies: generalized forces according to the Euler-Lagrange formalism

[adynak]

I am trying to derive the dynamic equations of an aerial vehicle with 6 degrees of freedom (a quadrotor to be precise). I am using

- two coordinate systems: the Earth frame and the body frame;
- the Euler-Lagrange formalism: generalized coordinates {x,y,z,phi,theta,psi}, respectively, the position in the Earth frame and the Tait-Brian (or ZYX) angles;
- I am considering the vehicle a rigid body.

My doubt is: when I write the generalized force vector (forces acting on the center of gravity and torques referred to the center of gravity) do I need to refer them to the Earth frame or to the body frame? In previous works I found out that the forces must be referred to the Earth frame, while the torques must be referred to the body frame ... but it does not make sense to me.

Could you please tell me the general formula for generalized forces when dealing with rigid bodies?

Thank you for your help,
Alex.

 

[Valerie Park]

The general formula for generalized forces when dealing with rigid bodies is the sum of the forces and moments applied to the body's center of mass, expressed in terms of the coordinates of the body frame. This means that the forces should be referred to the body frame, while the torques should be referred to the Earth frame.