Complex variable methods for linearized Euler rigid body rotation equations

Abstract

The determination of analytical solutions is a vital step in understanding the different physical systems and building confidence in the numerical methods that are required for more complex models. In the present work, analytical solutions are derived for axisymmetric and near-axisymmetric rigid body problems. The formulation proposed is based on a complex variable which characterizes all the different kinds of problems in similar terms. The described methodology is introduced for simple cases and, progressively, extended to other advanced problems such as random perturbations. As an application, this complex variable formulation can be used to characterize the asteroid’ motions, showing a dependence between their inertia coefficients and their rotational velocities when the asteroid is perturbed from its relaxed state. A Montecarlo experiment is done in order to determine how well the inertia ratios of the asteroid can be estimated knowing only information about its angular velocities.