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SYMPLECTIC LOOK AT SURFACES OF REVOLUTION
2003Given a surface of revolution in 3-space, there exist isothermal \(S^1\)-equivariant coordinates \((t,\theta)\) such that the metric is \(e^{\psi(t)}(dt^2+d\theta^2)\). Replacing \(t\) by the moment map \(\tau:=\int e^{\psi(t)}\,dt\) we get action angle coordinates \((\tau,\theta)\), and a function \(\phi(\tau)=e^{\psi(t)}\) called the momentum profile,
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Computing planar sections of surfaces of revolution with revolute quadric decomposition
Proceedings Shape Modeling Applications, 2004., 2004Computing the planar sections of objects is a fundamental operation in solid modeling. Subdivision method is commonly used for solving such intersection problems. In this paper, a revolute quadric decomposition is proposed for surfaces of revolution, which are subdivided into a set of coaxial revolute quadrics along the generatrix.
Jinyuan Jia 0002 +3 more
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An algorithm for geometrical modelling of surfaces of revolution
Computers & Graphics, 1986Abstract The main distinction of the new algorithm is its ‘friendliness.’ The user can choose to give certain information about the generating curve or just to move the cursor sufficiently close to the curve to be rotated, and not to give any additional information.
V. I. Fabrikant, T. S. Sankar
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Surface-of-revolution cosmology
Annals of Physics, 1972Abstract We investigate a cosmological model for which the three-geometry at any one time is represented by a three-dimensional surface of revolution, a concept explained in the body of the paper. For this model we write the Einstein equations and discuss their numerical solution.
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Willmore Surfaces of Revolution
2010This last chapter serves to give a first existence result for a priori bounded classical solutions of the Dirichlet problem forWillmore surfaces and thereby to outline possible directions of further research. In order to see which kind of phenomena and results concerning compact embedded solutions in R3 of boundary value problems for the corresponding ...
Filippo Gazzola +2 more
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Diffusion on Surfaces of Revolution
2012Diffusion processes play a fundamental role in mathematical models and simulation for particle and fluid dynamics, or heat transport. Many industrial devices have simple design, in particular the shape of surfaces of revolution. For sourceless diffusion on surfaces of revolution, we introduce a Hamiltonian system on a manifold and derive the governing ...
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Surface of revolution of a tool
1991Abstract Suppose that a tool moves with a predefined feed rate and simultaneously rotates around its axis of symmetry. In typical cases when the rotational speed is much higher than the feed rate we assume that a tool can be represented by the surface of revolution defined by the revolving edges of teeth.
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Isothermal Coordinate System on Surfaces of Revolution
Moscow University Mathematics BulletinzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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