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作者:Clementina D. Mladenova , Danail S. Brezov , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization2018Project Euclid
摘要:In the present paper we investigate an alternative two-axes decomposition method for rotations that has been proposed in our earlier research. It is shown to provide a convenient parametrization for many important physical systems. As an example, the kinematics of a rotating rigi...
作者:Vladimir I. Pulov , Mariana Ts. Hadzhilazova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization2018Project Euclid
摘要:We consider a class of linear Weingarten surfaces of revolution whose principal curvatures, meridional $k_{\mu}$ and parallel $k_{\pi}$, satisfy the relation $k_{\mu}=(n+1)k_{\pi}$, $n=0,\,1,\,2,\ldots\, .$ The first two members of this class of surfaces are the sphere $(n=0)$ an...
作者:Veliko D. Donchev , Clementina D. Mladenova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization2016Project Euclid
摘要:The Cayley maps for the Lie algebras $\mathfrak{su}(1,1)$ and $\mathfrak{so}(2,1)$ converting them into the corresponding Lie groups $\mathrm{SU}(1,1)$ and $\mathrm{SO}(2,1)$ along their natural vector-parameterizations are examined. Using the isomorphism between $\mathrm{SU}(1,1...
作者:Vladimir I. Pulov , Mariana Ts. Hadzhilazova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization2017Project Euclid
摘要:The plate-ball problem concerns the shortest trajectories traced by a rolling sphere on a horizontal plane between the prescribed initial and final states meaning the positions and orientations of the sphere. Here we present an explicit parametric representation of these trajecto...
作者:Danail S. Brezov , Clementina D. Mladenova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization2017Project Euclid
摘要:Here we develop a specific factorization technique for rotations in $\mathbb{R}^3$ into five factors about two or three fixed axes. Although not always providing the most efficient solution, the method allows for avoiding gimbal lock singularities and decouples the dependence on ...
作者:... Peter A. Djondjorov , Mariana Ts. Hadzhilazova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization2016Project Euclid
摘要:The work is concerned with a special family of axially symmetric surfaces providing local extrema to the so-called Willmore functional, which assigns to each surface its total squared mean curvature. The components of the position vector of the profile curves of the regarded Will...
作者:Veliko D. Donchev , Clementina D. Mladenova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization2017Project Euclid
摘要:The embeddings of the $\frak{so}(3)$ Lie algebra and the Lie group ${\rm SO}(3)$ in higher dimensions is an important construction from both mathematical and physical viewpoint. Here we present results based on a program package for building the generating matrices of the irreduc...
作者:Danail S. Brezov , Clementina D. Mladenova , Ivaïlo M. Mladenov
来源:[C].Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization2014Project Euclid
摘要:Here we use an extension of Rodrigues' vectorparameter construction for pseudo-rotations in order to obtainexplicit formulae for the generalized Euler decompositionwith arbitrary axes for the structure groups in the classicalmodels of hyperbolic geometry. Although the constructio...
作者:Ivaïlo M. Mladenov
来源:[C].Proceedings of the Fifth International Conference on Geometry, Integrability and Quantization2004Project Euclid
摘要:A few explicit formulas providing conformal coordinates of the axially symmetric constant mean curvature surfaces introduced by Delaunay and their duals are derived. These results give also new examples in a long line of research connected with finding isothermic immersions of su...

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