A discussion of time transformations and local truncation errors

Nacozy, P. E.

doi:10.1007/bf01229102

Cited by 17 publications

(9 citation statements)

References 15 publications

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“…Moreover, Sundman transformation can be used in the study of linearisation of differential equations [6] and in numerical solution of systems of differential equations (see e.g. [7][8][9][10][11]).…”

Section: Sundman Transformationmentioning

confidence: 99%

Infinitesimal Time Reparametrisation and Its Applications

Cariñena

Martínez

Muñoz-Lecanda³

2022

J Nonlinear Math Phys

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Section: Sundman Transformationmentioning

confidence: 99%

Infinitesimal Time Reparametrisation and Its Applications

Cariñena

Martínez

Muñoz-Lecanda³

2022

J Nonlinear Math Phys

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“…(23). In practice, the efficiency of one or another time transformation can depend not only on the model of acting forces and on the type of the orbit, but also on the applied method of numerical integration (Nacozy, 1976).…”

Section: Letmentioning

confidence: 99%

Application of a Fictitious Attracting Center to the Study of the Motion of Minor Bodies Approaching Major Planets

Shefer

2005

Sol Syst Res

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The motion of minor Solar System bodies having close encounters with major planets is described using the model of motion within the framework of the perturbed restricted three-body problem. The actual motion of a minor body is represented as a combination of two motions, namely, the motion of a fictitious attracting center with a variable mass and the motion with respect to the fictitious center. The position and mass of the fictitious center are chosen so that, when the minor body collides with any of the primaries, the fictitious center carries into the center of inertia of the colliding body and the mass of the fictitious center becomes identical to the mass of this body. The regularizing KS-transformation and Sundman's time transformation were applied to coordinates and velocities. As a result, a system of differential equations of motion that are quasilinear within the nearest vicinity of each of the primary attracting bodies was obtained. These equations are characterized by a numerical behavior during the encounters of the minor body with the primaries that is essentially better than that of the initial equations of motion. The motion of comets Brooks 2 and Gehrels 3, which have fairly close encounters with Jupiter, is simulated.

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“…Further discussions and references about the aspects of stabilization, uniformization of the local truncation error, and numerical error propagation related to the usage of a time transformation in the perturbed two-body problem can be found in Nacozy (1976a).…”

Section: Introductionmentioning

confidence: 99%

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

Baù

Bombardelli

2014

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We propose two time elements for the orbit propagator named Dromo. One is linear and the other constant with respect to the independent variable, which coincides with the osculating true anomaly in the Keplerian motion. They are defined from a generalized Kepler's equation written for negative values of the total energy and, unlike the few existing time elements of this kind, are free of singularities. To our knowledge it is the first time that a constant time element is associated with a second-order Sundman time transformation. Numerical tests to assess the performance of the Dromo method equipped with a time element show the remarkable improvement in accuracy for the perturbed bounded motion around the Earth compared to the case in which the physical time is a state variable. Moreover, the method is competitive with and even better than other efficient sets of elements. Finally, we also derive a time element for a null and positive total energy.

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A discussion of time transformations and local truncation errors

Cited by 17 publications

References 15 publications

Infinitesimal Time Reparametrisation and Its Applications

Infinitesimal Time Reparametrisation and Its Applications

Application of a Fictitious Attracting Center to the Study of the Motion of Minor Bodies Approaching Major Planets

Time Elements for Enhanced Performance of the Dromo Orbit Propagator

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