Matlab Program for Determining the Inertia Characteristics of Flat Surfaces with Monte Carlo Algorithms

Abstract

This paper presents a Matlab program for calculating the inertia tensor for complex plane surfaces. The calculation of the moments of inertia for plane surfaces with classical methods involves decomposing the surfaces into primitive surfaces and applying Steiner's relations. The classical methods are based on the knowledge of the analytical determined moments of inertia for primitive surfaces. In the case of complex surfaces, numerical methods can be used which are based on discretizing the surface into triangles and determining the moments of inertia by applying Steiner's relations knowing the analytical moments of inertia for a triangle. Both methods are computationally intensive and are basically based on the analytical moments of inertia of an elementary surface. In the case of large and complex surfaces the Monte Carlo algorithm can be used, which is a probabilistic algorithm based on the generation of area elements within the surface for  which the moments  of inertia are determined and then summed over the entire area bounded by the surface. The paper presents the Matlab calculation program and application examples for the use of the probabilistic Monte Carlo algorithm.