相关论文: A note on geodesics on ellipsoid

On Boxing Day, 1838, Jacobi found a solution to the problem of geodesics on a triaxial ellipsoid, with the course of the geodesic and the distance along it given in terms of one-dimensional integrals. Here, a numerical implementation of…

Closed geodesic lines on an ellipsoid in d-dimensional Euclidean space are considered. Explicit algebro-geometric condition for closedness of such a geodesic is given. The obtained condition is discussed in light of theta-functions theory…

This is the first part of a two-part paper describing a new concept of separation of variables applied to the Clebsch integrable case of the Kirchhoff equations. There are two principal novelties: 1) Separating coordinates are constructed…

In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, Editors: C.R.M.…

Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where…

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…

The algorithms given in Karney, J. Geodesy 87, 43-55 (2013), to compute geodesics on terrestrial ellipsoids are extended to apply to ellipsoids of revolution with arbitrary eccentricity. For the direct and inverse geodesic problems, this…

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…

In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new…

Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and…

The Lax representations of the geodesic flow, the Jacobi-Rosochatius problem and its perturbations by means of separable polynomial potentials, on a ellipsoid are constructed. We prove complete integrability in the case of a generic…

The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is a transcription of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825). The…

We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multivariable elliptic hypergeometric series are considered in…

Using the duplication formulas of the elliptic trigonometric functions of Gosper, we deduce some new special values for the first two Jacobi theta functions. At the end of the paper, we show how is it possible to extend our arguments and…

In this paper, we consider a spherically curved symmetric spacetime to exact solving the orbit equation of a massive particle by using Jacobi's elliptic functions. Generally, the solution of the orbit equation provides the relativistic…

Jacobi's elliptic functions have been constructed from a deformed Lie algebra. The generators of the algebra have been obtained from a bi-orthogonal system. The deformation parameter resembles the modulus of the relevant elliptic functions.

A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…

A universal method to solve the differential equations of light-like geodesics is developed. The validity of this method depends on a new theorem, which is introduced for light-like geodesics in analogy to Beltrami's "geometrical" method…