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Galaxies 2017, 5(4), 101; doi:10.3390/galaxies5040101

Explicit Second Partial Derivatives of the Ferrers Potential

1
Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, IFSP, São José dos Campos 12.223-201, Brazil
2
Physics and Astronomy Laboratory, Universidade do Vale do Paraíba, UNIVAP, São José dos Campos 72840, Brazil
3
Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE, Puebla, Mexico
*
Author to whom correspondence should be addressed.
Received: 3 November 2017 / Revised: 4 December 2017 / Accepted: 5 December 2017 / Published: 15 December 2017
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Abstract

One of the algebraic potentials most commonly used to represent a galactic bar in the stellar orbits integration is the Ferrers potential. Some researchers may be inclined to implement a numerical differentiation for it in the motion or variational equations, since it can be very laborious to calculate such derivatives algebraically, despite a possible polynomial form, and there are no publications showing the second partial explicit derivatives. The purpose of this work is to present the explicit algebraic form of the partial derivatives of the Ferrers potential using the simplifications suggested by Pfenniger. View Full-Text
Keywords: galactic dynamics; galaxies barred; orbits integration; gravitational potential galactic dynamics; galaxies barred; orbits integration; gravitational potential
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Caritá, L.A.; Rodrigues, I.; Puerari, I. Explicit Second Partial Derivatives of the Ferrers Potential. Galaxies 2017, 5, 101.

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