Collision Course for Objects Moving on a Spherical Manifold

TL;DR

This paper introduces a novel framework for predicting collisions of objects moving on a spherical surface by defining collision triangles and deriving analytical conditions for collision scenarios.

Contribution

It develops the concept of collision triangles on spherical manifolds and derives analytical conditions for collisions involving point and circular patch objects.

Findings

Defined collision triangles on spherical manifolds

Derived analytical collision conditions for point objects

Extended conditions to circular patch objects

Abstract

In this paper, we address the problem of predicting collision for objects moving on the surface of a spherical manifold. Toward this end, we develop the notion of a collision triangle on such manifolds. We use this to determine analytical conditions governing the speed ratios and direcions of motion of objects that lead to collisions on the sphere. We first develop these conditions for point objects and subsequently extend this to the case of circular patch shaped objects moving on the sphere.