Stochastic modeling of uncertain mass characteristics in rigid body dynamics. (15th March 2017) - Richter, Lanae A.; Mignolet, Marc P.
Abstract: This paper focuses on the formulation, assessment, and application of a modeling strategy of uncertainty on the mass characteristics of rigid bodies, i.e. mass, position of center of mass, and inertia tensor. These characteristics are regrouped into a 4×4 matrix the elements of which are represented as random variables with joint probability density function derived following the maximum entropy framework. This stochastic model is first shown to satisfy all properties expected of the mass and tensor of inertia of rigid bodies. Its usefulness and computational efficiency are next demonstrated on the behavior of a rigid body in pure rotation exhibiting significant uncertainty in mass distribution. Highlights: Modeling of uncertainty in mass and inertias of rigid bodies is achieved in one computation. All properties of mass and inertias, e.g., positive definiteness, parallel axis theorem, transformation under rotation of frame, are respected for all samples. The modeling is expediently accomplished using only the properties of the mean model and a single measure of the uncertainty level. Validation example is presented that demonstrate the ease of application and potential.