Introduction To Lagrangian Dynamics by Aron Wolf Pila

Author:Aron Wolf Pila
Language: eng
Format: epub, pdf
ISBN: 9783030223786
Publisher: Springer International Publishing

D’Alembert–Lagrangian Dynamics

Defining the generalized coordinates to be: q = (X, Y, Z, ψ, θ, ϕ), where is the position vector from the origin of the inertial coordinate system to the center of mass of the quadrotor (in inertial coordinates) and η = (ψ, θ, ϕ) are the Euler angles around the yaw (around the ), pitch (around the ), and roll (around the ) axes, respectively, which define the orientation of the quadrotor with respect to the inertial coordinate system. The kinetic energy has a translational component as well as a rotational part. The derivatives of the Euler angles are: . The rotational kinetic energy is of the form: . Since the angular rates have not been measured along the quadrotor’s body axes, the full inertia tensor must be used in the computation of rotational kinetic energy, and it is:

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