Publication

Analytical calculation of the inertia matrices of convex spheropolyhedra

Lionel Pournin
2008
Reports

Abstract

Spheropolyhedra are bodies obtained as Minkowski sums of polyhedra with spheres. They are simple, yet flexible models of non-spherical particles for granular media simulated with the Distinct Element Method (DEM). We here give an analytical method for the calculation of the inertia matrices of convex spheropolyhedra. The special cases of regular spherotetrahedra and arbitrary spherotriangles are addressed and explicit expressions of their inertia matrices are given.

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Lionel Pournin
2008
Reports

Abstract

Official source

Related concepts (32)

Polyhedron

In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.

Sphere

A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. The sphere is a fundamental object in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry.

List of uniform polyhedra

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both.

Related publications (1)

Analytical calculation of the inertia matrices of convex spheropolyhedra

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