Center of Mass Technique and Affine Geometry
From MaRDI portal
Publication:6510777
DOI10.46298/CM.11527arXiv2306.15099MaRDI QIDQ6510777
Author name not available (Why is that?)
Abstract: The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for sets whose total mass equals zero. In the paper we improve this disadvantage and assign to an n-dimensional affine space L over any field k the (n+1)-dimensional vector space over the field k of weighty points and mass dipoles in L. In this space, the sum of weighted points with nonzero total mass is equal to the center of mass of these points equipped with their total mass. We present several interpretations of the space of weighty points and mass dipoles in L, and a couple of its applications to geometry. The paper is self-contained and is accessible for undergraduate students.
No records found.
This page was built for publication: Center of Mass Technique and Affine Geometry
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6510777)
