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Parabolic and Non-Parabolic Loci of the Center of Gravity of Variable Solids
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| Organization: | Southeastern Louisiana University |
| Department: | Department of Mathematics |
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2003 International Mathematica Symposium
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Imperial College, London
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Consider certain types of solids S in three-dimensions with a variable boundary. It is assumed that this boundary changes with two real parameters s and t. Examples of such include solids bounded by a fixed elliptic cylinder and a variable plane, solids bounded by a fixed elliptic paraboloid and a variable plane, and also solids bounded by a fixed astroidal cylinder and a variable plane. Let G(x, y, z) denote the center of gravity of the solid S. As the parameters s and t change, this center of gravity G changes. According to some of the previous studies, for several well-known types of solids S, the locus of G is a paraboloid in three-dimensions. In this paper, we will further investigate such locus problems. In particular, it is of interest to discover familiar types of variable solids, for which the locus of the center of gravity G is not a paraboloid. In order to calculate the triple integrals associated with these center of gravity problems, and also to create visualizations of the loci, one can effectively use Mathematica.
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parabolic and non-parabolic loci, variable solids, center of gravity
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