SOME MATHEMATICAL CONCEPTS IN GEOMETRY OF MASSES

  • Gordana Jelić Faculty of Technical Sciences, University of Priština, Kosovska Mitrovica, Serbia
  • Dejan Stošović Faculty of Technical Sciences, University of Priština, Kosovska Mitrovica, Serbia
Keywords: Material point, Geometry of masses, Body density, Linear density, Surface density, Homogeneous material, Non-homogeneous materials, Center of mass

Abstract


The study of the distribution of geometrical points, loaded by some scalars plays an important role in various fields of science, of theoretical and practical character. Since such study was first applied and studied when mass had the role of played a scalar, the mass loaded point was named material point, and the discipline dealing with the arrangement of material points in space is called the geometric mass. In that discipline, in the general case under mass one should imply a scalar of arbitrary nature, which can be negative as well. For example, the discipline includes the study of distribution of magnetic or electrical masses, which can be positive and negative. This paper presents some concepts from the geometry of masses that play an important role, particularly in mechanics and physics.

References

Awrejcewicz, J. 2012. In: Classical Mechanics, Springer, pp. 131-185.

Bessonov, N. M., & Song, D. J. 2001. Application of vector calculus to numerical simulation of continuum mechanics problems. Journal of Computational Physics, 167(1), pp. 22-38.

Bilimović, A. 1961. Integralni račun sa primenama.

Dorogovtsev, A. Y. 1987. Mathematical analysis: Collection of problems. Vishcha school.

Mirtich, B. 1996. Fast and accurate computation of polyhedral mass properties. Journal of graphics tools, 1(2), pp. 31-50.

Whitaker, S. 1992. The species mass jump condition at a singular surface. Chemical Engineering Science, 47(7), pp. 1677-1685.

Published
2020/11/09
Section
Original Scientific Paper