Some Critical Issues in Application of Lagrangian Mechanics to Air Vehicles Analysis: An Example of Quadrotor

Abstract

For a mechanical system, the correct derivation of equations of motion is extremely important for modeling such as an air vehicle. It is necessary to correctly determine the dynamic equations representing the motion of the air vehicle to be analyzed. Then applying a solution method to be sure that will provide high-accuracy results and by using these results more realistic simulation can be given. In this article; in the open literature, some errors which are commonly made are depicted when the Lagrangian mechanics approach, which is one of the classical mechanic methods, to apply to analyze some mechanical problems. To obtain the equations of motion, that can be used to describe the behavior of the mechanical system, there is an error in the application of the order of angular rotational equations. This study considers the derivations of angular motions of a mechanical system in the correct order, otherwise, the equations obtained cannot correctly represent the behavior of the mechanical systems. Therefore, a quadrotor system has been chosen as an example and its equations of motion have been derived in the correct order. And the differences between the correct one and the erroneous one are indicated. Also, the others that come across in open literature are addressed. To satisfy the way, which is used in the derivations, Newtonian Mechanics are also applied the same problems to show the same results as the ones obtained by Lagrangian mechanics. The paramount importance of this study is to serve for the researchers to prevent commonly made mistakes in applications of Lagrangian mechanics for mechanical systems. Also, while modeling non-linear mechanical systems, with complex translational and rotational equations such as air vehicles by using Lagrange mechanics can be safely obtained.