• Corpus ID: 41449452

# Geodesics on the Torus and other Surfaces of Revolution Clarified Using Undergraduate Physics Tricks with Bonus: Nonrelativistic and Relativistic Kepler Problems

@article{Jantzen2012GeodesicsOT,
title={Geodesics on the Torus and other Surfaces of Revolution Clarified Using Undergraduate Physics Tricks with Bonus: Nonrelativistic and Relativistic Kepler Problems},
author={Robert T. Jantzen},
journal={arXiv: Differential Geometry},
year={2012}
}
• R. Jantzen
• Published 26 December 2012
• Physics
• arXiv: Differential Geometry
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by interpreting parametrized geodesics as the paths traced out in time by the motion of a point in the surface, identifying the parameter with the time. Considering energy levels in an effective potential for the reduced motion then proves to be an extremely useful…

## Figures from this paper

Cavatappi 2.0: More of the same but better
Innocent musing on geodesics on the surface of helical pasta shapes leads to a single continuous 4-parameter family of surfaces invariant under at least a 1-parameter symmetry group and which
Numerical Approach for Fermat's last theorem
This research focuses on the Numerical approach for Fermat's Last theorem. We can induce an Alternative form of Fermat's last theorem by using particular geometric mapping $\mathcal{M}$ on a
Magnetic curves in the real special linear group
• Mathematics
Advances in Theoretical and Mathematical Physics
• 2019
We investigate contact magnetic curves in the real special linear group of degree 2. They are geodesics of the Hopf tubes over the projection curve. We prove that periodic contact magnetic curves in
Star formation in extreme environments
The study of star formation bridges many vastly disparate scales. From the small, nearby, quiescent cores of low mass star formation, to the highly turbulent conditions in which the most massive
On some Closed Magnetic Curves on a 3-torus
• Mathematics
• 2017
We consider two magnetic fields on the 3-torus obtained from two different contact forms on the Euclidean 3-space and we study when their corresponding normal magnetic curves are closed. We obtain
Phonon Guided Biology. Architecture of Life and Conscious Perception Are Mediated by Toroidal Coupling of Phonon, Photon and Electron Information Fluxes at Discrete Eigenfrequencies.
• Physics
• 2016
Recently, a novel biological principle, revealing specific electromagnetic (EM) radiation frequencies that sustain life, was presented by us on the basis of an evaluation of 175 biological articles
Why Curves Curve: The Geodesics on the Torus
• Physics
Mathematics Magazine
• 2022
Abstract Based on an intuitively appealing way of defining what is meant by a geodesic on a two-dimensional surface in three-dimensional Euclidean space, we describe the general behavior of the

## References

SHOWING 1-10 OF 11 REFERENCES
Differential Geometry and Its Applications
Preface. 1. The Geometry of Curves. Introduction. Arclength Parametrization. Frenet Formulas. Nonunit Speed Curves. Some Implications of Curvature and Torsion. The Geometry of Curves and MAPLE. 2.
Differential Geometry of Curves and Surfaces
• Mathematics
• 2010
Plane Curves: Local Properties Parametrizations Position, Velocity, and Acceleration Curvature Osculating Circles, Evolutes, and Involutes Natural Equations Plane Curves: Global Properties Basic
Elementary Differential Geometry
Curves in the plane and in space.- How much does a curve curve?.- Global properties of curves.- Surfaces in three dimensions.- Examples of surfaces.- The first fundamental form.- Curvature of
Random geometric graphs, their properties and applications on the plane, sphere, and torus
• Mathematics
• 2010
I have investigated the evolution of random geometric graphs' properties. The focus has been given to chromatic number, maximum clique size and independent sets. I have devised algorithms and
The General relativistic Poynting-Robertson effect
• Physics
• 2008
The general relativistic version is developed for Robertson's discussion of the Poynting–Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like
Introduction to General Relativity
Gravity is not a force of foreign origin transmitted through space and time. Gravity is a manifestation of the curvature of space time. That is Einstein’s account of gravity in brief.
Elementary Differential Geometry
Elementary Differential Geometry, Second Edition provides an introduction to the geometry of curves and surfaces.
The CRC concise encyclopedia of mathematics
Terms related to mathematics, physics, biochemistry, chemistry, biophysics and engineering organized alphabetically, including definition, formula, illustration, and bibliographic information.
The Curvature and Geodesics of the Torus
• http://www.rdrop.com/∼half/math/torus/torus.geodesics.pdf
• 2005