Jacobi Conformal Projection of the Triaxial Ellipsoid: New Projection for Mapping of Small Celestial Bodies

Nyrtsov, M.V.; Fleis, Maria E.; Borisov, M. M.; Stooke, P. J.

doi:10.1007/978-3-642-32618-9_17

Cited by 17 publications

(8 citation statements)

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“…215-217 of second edition). Jacobi's map was implemented recently in [31] and [19]. Isothermal coordinates (u, v) on an octant of E 2 can be constructed using elliptic integrals of the third kind Π (see [5])…”

Section: Adriano Regis Rodrigues César Castilho and Jair Koillermentioning

confidence: 99%

Vortex pairs on a triaxial ellipsoid and Kimura's conjecture

Rodrigues¹,

Castilho²,

Koiller³

2018

Journal of Geometric Mechanics

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We consider the problem of point vortices moving on the surface of a triaxial ellipsoid. Following Hally's approach, we obtain the equations of motion by constructing a conformal map from the ellipsoid into the sphere and composing with stereographic projection. We focus on the case of a pair of opposite vortices. Our approach is validated by testing a prediction by Kimura that a (infinitesimally close) vortex dipole follows the geodesic flow. Poincaré sections suggest that the global flow is non-integrable.

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Section: Adriano Regis Rodrigues César Castilho and Jair Koillermentioning

confidence: 99%

Vortex pairs on a triaxial ellipsoid and Kimura's conjecture

Rodrigues¹,

Castilho²,

Koiller³

2018

Journal of Geometric Mechanics

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“…Thus, it is possible to control the results obtained with use of equation (4) by using the equation for the length of a meridian on a triaxial ellipsoid expressed by planetocentric or planetographic coordinates. Using the derived equation (4) (Nyrtsov at al., 2014). First of all, the reduced and planetocentric coordinates were calculated for 16 points located on a triaxial ellipsoid.…”

Section: The Results Of Calculations Of the Lengths Of Meridiansmentioning

confidence: 44%

“…Using other ways of parameterization of a triaxial ellipsoid may simplify the process of creating map projections and enable a more aesthetic form of the functions. For example Nyrtsov (2014) used ellipsoidal coordinates to create conformal projection of a triaxial ellipsoid and Bugayevsky (1991) used isometric coordinates for the same purpose. The author of this paper propose to use reduced coordinates in equidistant map projections.…”

Section: Introductionmentioning

confidence: 43%

“…Snyder (1985) presented the triaxial equivalent of the Mercator projection. Different versions of conformal projections of a triaxial ellipsoid were created by Nyrtsov (2014), who developed such a projection with use of elliptical coordinates. Fleis et al (2013) presented a conformal projection that maintained the angle between parallels and meridians.…”

Section: Introductionmentioning

confidence: 45%

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Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

Pędzich¹

2017

Geodesy and Cartography

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Abstract:The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

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“…The CPN generation is complicated by irregular shape of many celestial bodies, which should be better approximated by 3-axial ellipsoids. This requires an individual approach for the special projection for small bodies (Bugaevsky et al 1992;Nyrtsov et al 2014) and implementation of special tools (http://geocnt.geonet.ru//en/3_axial) supporting a 3-axial reference surface. In addition, information about shape and size of planets and their satellites is being constantly updated, which affects the best-fit ellipsoid parameters.…”

Section: Coordinate Systems Of Celestial Bodiesmentioning

confidence: 44%

Modern Methodology and New Tools for Planetary Mapping

Karachevtseva

Kokhanov

Zubarev

et al. 2016

Lecture Notes in Geoinformation and Cartography

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The paper describes a workflow of planetary mapping using the newest remote sensing data and modern GIS technologies. We present the newly developed tools for planetary surface analysis based on cartographic measurements. The data management and design approaches for planetary mapping are described, and the main results of implementation of tools and methods are presented, including new planetary maps.

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Jacobi Conformal Projection of the Triaxial Ellipsoid: New Projection for Mapping of Small Celestial Bodies

Cited by 17 publications

References 1 publication

Vortex pairs on a triaxial ellipsoid and Kimura's conjecture

Vortex pairs on a triaxial ellipsoid and Kimura's conjecture

Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

Modern Methodology and New Tools for Planetary Mapping

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