Abstract The centre of mass (CM) is a key concept that facilitates the understanding various physics topics and solution problems. This study’s aim to present an activity for students experimentally determine location CM bodies with outside body. Thus, example will be presented allow understand situation where body, find bodies, generate new examples body themselves. For at-rest common experime...

This paper gives various (positive and negative) results on the complexity of the problem of computing and approximating mixed volumes of polytopes and more general convex bodies in arbitrary dimension. On the negative side, we present several #P-hardness results that focus on the difference of computing mixed volumes versus computing the volume of polytopes. We show that computing the volume o...

The topological relation is one of the most important spatial relations. Analysis of spatial relation has great practical value. The possible topological relations between 3D simple body objects can be analyzed using 9-intersection model. An algorithm is proposed to analyze the topological relations between body objects. It decomposes the complicated objects into simple objects, so it can get t...

The network reduction systen of RAPT, an o f f l ine object level language for programming robot assembly tasks is described in this paper. The task description is converted into a relat ional network with the positions of bodies as nodes, and rela­ tionships between positions as l inks. Rewrite rules based on the intersection and conposition of relations are used to simplify the network.

We propose a mathematical model for m-dimensional nonlinear hyperelastic bodies moving in R for all m ≤ n, which enables frictionless contacts or self-contacts but not (self-)intersection. To this end, we de ne a set of admissible deformations, and prove the existence of at least one minimizer of the energy, under suitable assumptions on the stored energy. Moreover, we give a partial equivalenc...

– The Brunn-Minkowski theory is a central part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Its origins were in Minkowski’s joining his notion of mixed volumes with the Brunn-Minkowski inequality, which dated back to 1887. Since then it h...

A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a “fat” one, if it contains the centers of its generating balls. The main result of this paper is a proof of the Illumination Conjecture for “fat” spindle convex b...

We study two notions. One is that of lens-convexity. A set of circumradius not greater than one is lens-convex if, for any pair of its points, it contains every shorter unit circular arc connecting them. The other objects of study are bodies obtained as an intersection of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on convex polyhedral set...