Abstract
We will present 2 different analytical representations of only one general idea—this is the representation of complex movements using the superposition of certain elementary displacements! Despite of the analytical and structural similarity of these representations, they describe fundamentally different geometric figures (in statics) and trajectories of motion (in dynamics). In previous articles [1,2,3,4,5,6,7,8,9] a wide class of geometric figures—“Generalized Twisting and Rotated” bodies \(GRT^n_m\) in short—was defined through their analytic representation. In particular cases, this analytic representation gives back many classical objects (torus, helicoid, helix, Möbius strip ... etc.). The aim of this article is to consider some geometric properties of a wide subclass of the generally defined surfaces. We show some geometric properties of GRT and GML—surfaces.
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Tavkhelidze, I., Gielis, J., Pinelas, S. (2020). About Some Methods of Analytic Representation and Classification of a Wide Set of Geometric Figures with “Complex” Configuration. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_27
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