Derivação das equações de movimento de corpo em rotação sob momento de força da forma geral

Abstract

In the standard approach to the rigid body dynamics, the equations of motion are usually (and in fact intuitively) postulated and then studied in the one or another bodyfixed frame. Then the final results of analysis should be translated into the Laboratory frame, where the body is observed. Because of this intuitive and indirect procedure, the original equations are sometimes taken incorrect. The known examples are the equations of a Lagrange top and of a dancing spinning (or Poisson) top. Besides, when analyzing them, some subtleties of rigid body dynamics are sometimes not taken into account, leding to wrong final conclusions. So in the present dissertation we proceed in a more direct way, according to the recently developed formalism (1). We derive the rigid-body equations in the framework of standard methods of classical mechanics adapted and applied to the rigid body considered as a system of particles with holonomic constraints. We work in terms of the rotation matrix, which contains all information on the movement with respect to the Laboratory frame, by writting the equations of motion for all involved dynamical variables parameterized in the Laboratory frame. The main focus will be on the derivation of equations with the external torque of the force of a general form.