Earth’s Rotation: A Challenging Problem in Mathematics and Physics

Ferrándiz, José M.; Navarro, Juan F.; Escapa, Alberto; Getino, Juan

doi:10.1007/s00024-014-0879-7

Cited by 9 publications

(7 citation statements)

References 79 publications

(44 reference statements)

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“…There are hundreds, perhaps thousands, of papers, surveys, and proposed ideas discussing a very wide range of issues relating to Earth, astronomy, and IoT knowledge [39][40][41][42]. However, as we searched extensively for related works to ours, we found that no previous work discussed the computation of net force produced by actuators on Earth conceptually as described in this paper.…”

Section: State Of the Art Of Evaluation Methodologies In Iot Systemsmentioning

confidence: 97%

GRAFT: A Model for Evaluating Actuator Systems in Terms of Force Production

Baniata

Sharieh

Mahmood

et al. 2020

Sensors

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In the scope of evaluation methodologies for Internet of Things (IoT) systems, some approaches concern security, while others latency. However, some methodologies evaluate systems that contain active entities, so-called actuators. In this paper, we propose a novel methodology for evaluating such systems with actuator components using Graph Representation of the Angle of the Force and Time (GRAFT). GRAFT facilitates easy computation of the net force produced by physical or mechanical acts occurring on a daily basis on Earth. We use laws and definitions of physics describing the relations between Speed, Distance, and Time (SDT), apply them in a heliocentric system, and model the considered systems with a graph. The continuous movement of the Earth was shown to be weakening the total produced net force in some systems. We considered this weakening issue a problem, and we propose two possible solutions to overcome it by using restoration values, or reordering actuator sessions, in GRAFT to arrive to a more force-efficient system. We compared our default GRAFT algorithm to a special implementation using the Clock-Angle-Problem (CAP) for sessions. We also study and discuss an IoT-focused case for validating our approach, and we present a detailed explanation of the proposed GRAFT algorithm. The experimental results show the ability of GRAFT to provide highly accurate results, which also exemplifies that our GRAFT approach is programmable, hence deployable in real life scenarios.

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Section: State Of the Art Of Evaluation Methodologies In Iot Systemsmentioning

confidence: 97%

GRAFT: A Model for Evaluating Actuator Systems in Terms of Force Production

Baniata

Sharieh

Mahmood

et al. 2020

Sensors

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“…For the sake of concreteness, the periodic part of the former first order solution will be obtained. From an astronomical point of view, this is related to the forced nutations of the Earth (see e.g., Ferrándiz et al 2015).…”

Section: Application Of the Modified Lie-hori Methodsmentioning

confidence: 99%

Application of first-order canonical perturbation method with dissipative Hori-like kernel

Baenas

Escapa

Ferrándiz

et al. 2017

International Journal of Non-Linear Mechanics

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Lie-Hori canonical perturbation theory provides asymptotic solutions for conservative Hamiltonian systems. This restriction prevents the canonical method from being applied directly to dissipative mechanical systems. There are, however, two main alternatives to overcome this difficulty, enabling the application of canonical perturbation methods. The first one consists in constructing a timedependent Hamiltonian, through a generating function, related to the energy dissipation pattern of the system. The second embeds the original phase space into a double dimensional one where the dynamics of the system can be formulated in a Hamiltonian way. In this paper, a modified Lie-Hori method that avoid the disadvantages of the former approaches is proposed. Namely, it is not necessary to find out a time-dependent generating function, nor doubling the number of the canonical variables of the original problem. The new algorithm provides first order analytical solutions for a certain set of dissipative non-linear dynamical systems. It is based on a suitable modification of the Hori kernel in the double-dimensional embedding phase space, allowing the inclusion of the dissipative (or generalized) forces. By means of this redefined auxiliary system, the path-integrals of the method can be performed in a domain of the phase space with the same dimensionality as the original problem.

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“…Let us start by recalling the formulae for the Poisson and Oppolzer terms due to the zonal component (2, 0) of the direct lunisolar potential in the case of a rigid Earth. We employ the same notation used in Getino & Ferrándiz (1995) and Ferrándiz et al (2016), similar to the original notation used by Kinoshita (1977). For the sake of conciseness, our notation is not explained here in detail, since the main difference with respect to Kinoshita's one lies in the notation of the Andoyer variables as (λ, µ, ν, Λ, M, N) instead of (h, g, l, H, G, L), and the use of σ instead of J for the colatitude of the angular momentum axis.…”

Section: Computation Of Oppolzer Terms In the Planetary Nutationsmentioning

confidence: 99%

“…In this context, the Poisson terms raised by a perturbing body B p of Kinoshita's constant K p can be written (Getino & Ferrándiz 1995;Ferrándiz et al 2016) as…”

Section: Computation Of Oppolzer Terms In the Planetary Nutationsmentioning

confidence: 99%

Limitations of the IAU2000 nutation model accuracy due to the lack of Oppolzer terms of planetary origin

Ferrándiz

Navarro

Martínez-Belda

et al. 2018

A&A

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Context. The current IAU2000 nutation model performed different approximations, one of them being that the Oppolzer terms associated to the planetary perturbations of the nutations were assumed to be smaller than 5 μas and thus were neglected. At present, the uncertainties of the amplitudes of individual components of the observed nutations are better, and the conventional nutation model does not fit the accuracy requirements pursued by the International Astronomical Union (IAU) and the International Association of Geodesy (IAG). Aims. The objective of this work is to estimate the magnitude of the lacking Oppolzer terms of the planetary nutations and find out whether they are still negligible or not. Methods. The Oppolzer terms resulting from the direct and indirect planetary perturbations of the Earth’s rotation have been computed for a two-layer Earth model following the Hamiltonian theory of the non-rigid-Earth. Results. The planetary Oppolzer terms for the non-rigid Earth are not really negligible as believed, and some of them have amplitudes larger than 10 μas, therefore significantly above the current level of uncertainty of individual harmonic constituents. Conclusions. In the short term, the IAU2000 nutation model must be supplemented with suitable corrections accounting for those missing components; its planetary component must be thoroughly revised in the medium term.

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Earth’s Rotation: A Challenging Problem in Mathematics and Physics

Cited by 9 publications

References 79 publications

GRAFT: A Model for Evaluating Actuator Systems in Terms of Force Production

GRAFT: A Model for Evaluating Actuator Systems in Terms of Force Production

Application of first-order canonical perturbation method with dissipative Hori-like kernel

Limitations of the IAU2000 nutation model accuracy due to the lack of Oppolzer terms of planetary origin

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