ISSN:
1435-5663
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Technology
Notes:
Abstract This paper concerns several analytical problems related to linear polyhedra in euclidean three-dimensional-space. Symbolic formulas for line, surface, and volume integration are given, and it is shown that domain integrals are computable in polynomial time. In particular, it is shown that mass, first and second moments, and products of inertia are computable inO(E) time, whereE is the number of edges of the boundary. Simple symbolic expressions for the normal derivatives of domain integrals are also derived. In particular, it is shown that they are closely linked to the topology of the integration domain, as well as that they are expressible as combinations of domain integrals over lower-order domains (faces, edges, and vertices). The symbolic results presented in this paper may lead to an easy incorporation of integral constraints, for example, concerning mass and inertia, in the engineering designing process of solid objects.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01200201
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