Hansen's Method of Partial Anomalies: an Application

Nacozy, P. E.

doi:10.1086/110833

Cited by 22 publications

(11 citation statements)

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“…This method involves the division of a cometary orbit into several (at least two) parts with its own independent argument for each part. In spite of all efforts of Gylden and his followers the partial anomaly technique remained and still remains rather cumbersome for wide application (Nacozy, 1969;Skripnichenko, 1972). Since then the idea of Gylden was regarded only as an attempt to improve the partial anomaly technique and numerical integration became the most widespread tool for investigation of the cometary motion.…”

Section: Compact-form Series In Classical Celestial Mechanicsmentioning

confidence: 99%

Theory compression with elliptic functions

Brumberg¹

1996

Symp. - Int. Astron. Union

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Section: Compact-form Series In Classical Celestial Mechanicsmentioning

confidence: 99%

Theory compression with elliptic functions

Brumberg¹

1996

Symp. - Int. Astron. Union

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“…This method improves its convergence using two new anomalies Ψ 1 and Ψ 2 depending of the region of the orbit that is occupied by the secondary [16].…”

Section: Introductionmentioning

confidence: 99%

An improved algorithm to develop semi-analytical planetary theories using Sundman generalized variables

Ortí

Agost-Gómez

Barreda-Rochera

2015

Journal of Computational and Applied Mathematics

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One of the main problems in celestial mechanics is the construction of the analytical theories of planetary motion. The most common solution of this problem is arranged by means of Poisson series developments. These developments depend on the selection of the anomaly to be used as temporal variable. In this paper we develop an improved alghoritm in order to use of an arbitrary anomaly included in the family of the generalized Sundman anomalies as temporal variables.

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“…To solve this problem, Hansen introduced a new set of temporal variables known as partial anomalies, and with these variables, we can obtain developments that are rapidly convergent. This method was extended by Nacozy [12].…”

Section: Introductionmentioning

confidence: 99%

A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics

Ortí

Gómez

Rochera

2012

International Journal of Computer Mathematics

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The main aim of this paper is to build up a set of semi-analytical integrators based on the use of a class of anomalies defined by means of a generalized Sundman transformation. The integrators are based on the developments of the mean anomaly and the vector radius according to the new anomaly. To manipulate these developments, a Poisson series processor called poison.h has been used. This processor has been written as a C++ class and it contains a set of methods to manage the most common arithmetic and functional operations with these objects.

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Hansen's Method of Partial Anomalies: an Application

Cited by 22 publications

References 0 publications

Theory compression with elliptic functions

Theory compression with elliptic functions

An improved algorithm to develop semi-analytical planetary theories using Sundman generalized variables

A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics

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