About the Free and Forced Nutation: The Daily Nutation

Monica Zoe Ciobanu

doi:doi:10.11648/j.ajaa.20210902.12

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About the Free and Forced Nutation: The Daily Nutation

Monica Zoe Ciobanu

Published in American Journal of Astronomy and Astrophysics (Volume 9, Issue 2)

Received: 22 March 2021 Accepted: 14 April 2021 Published: 8 May 2021

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Abstract

To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.

Published in	American Journal of Astronomy and Astrophysics (Volume 9, Issue 2)
DOI	10.11648/j.ajaa.20210902.12
Page(s)	18-21
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Nutation, Euler-Poinsot Case, Earth-Moon Barycenter

References

[1]	L. Euler, Theoria motus corporum solidorum sei ridigorum, 1790.
[2]	E. W. Woolard, Astronomical Papers, American Ephemeris, Nautical Almanach, XV, Part. 1, pg. 1-165, 1953.
[3]	V. Vâlcovici, şt. Bălan, R. Voinea, Mecanica Teoretică, Editura Tehnică, Bucureşti, 1963.
[4]	L. Poinsot, Théorie nouvelle de la rotation des corps, Paris 1834.
[5]	A. M. Liapunov, The general problem of stability of motion (in Russian), Doctoral dissertation, Univ. of Kharkov, 1892.
[6]	S. Chandler; On the variation of latitude, VIII, Astron. J., 13, 1893.
[7]	P. Melchior, Physique et Dynamique Planétaires, Vander, Bruxelles, 1971.
[8]	P. P. Teodorescu, Probleme spaşiale în teoria elasticităşii, Edit. Academiei, Bucuresti, 1970.
[9]	M. Ciobanu, Cas particulier dans le movement d’un corps deformable avec un point fix. Le cas de la Terre. Romanian Astronomical Journal Vol. 1, No 1-2, Bucharest, 1991.
[10]	M. Z. Ciobanu, A Rigorous Astrometrical Solution in the Case of the Euler-Poinsot Equations System, Vol. 29, 2019. Available from: http://www.astro.ro/~roaj/29_2/10-mciobanu_1905.pdf.
[11]	International Earth Rotation and Reference System Publications.
[12]	N. N. Pariiskii, The discovery of the Earth‘s diurnal nutation, Quatrième Symposium international sur les marées terrestres, Bruxelles, 1961.
[13]	C. Sugawa, On the Lunar tidal effect in the latitude observations at Mizusawa, Publ. Int. Lat. Obs. Mizusawa, 3, No. 2, 121, 1961.
[14]	S. Debarbat, Nearly Diurnal Nutation and Periodic Terms in Local Coordinates, Astron. & Astrophys., 1969.
[15]	M. Z. Ciobanu, Andrei Dihore, Similitude between the Earth’s nucleus and the Earth-Moon barycenter. Available from: http://ojs.whioce.com/index.php/eoaa/article/view/1209.

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Monica Zoe Ciobanu. (2021). About the Free and Forced Nutation: The Daily Nutation. American Journal of Astronomy and Astrophysics, 9(2), 18-21. https://doi.org/10.11648/j.ajaa.20210902.12

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Monica Zoe Ciobanu. About the Free and Forced Nutation: The Daily Nutation. Am. J. Astron. Astrophys. 2021, 9(2), 18-21. doi: 10.11648/j.ajaa.20210902.12

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Monica Zoe Ciobanu. About the Free and Forced Nutation: The Daily Nutation. Am J Astron Astrophys. 2021;9(2):18-21. doi: 10.11648/j.ajaa.20210902.12

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@article{10.11648/j.ajaa.20210902.12,
  author = {Monica Zoe Ciobanu},
  title = {About the Free and Forced Nutation: The Daily Nutation},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {2},
  pages = {18-21},
  doi = {10.11648/j.ajaa.20210902.12},
  url = {https://doi.org/10.11648/j.ajaa.20210902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210902.12},
  abstract = {To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.},
 year = {2021}
}

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TY  - JOUR
T1  - About the Free and Forced Nutation: The Daily Nutation
AU  - Monica Zoe Ciobanu
Y1  - 2021/05/08
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210902.12
DO  - 10.11648/j.ajaa.20210902.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 18
EP  - 21
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210902.12
AB  - To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.
VL  - 9
IS  - 2
ER  -

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Author Information

Monica Zoe Ciobanu

Astronomical Institute of the Romanian Academy, Bucharest, Romania

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APA Style

Monica Zoe Ciobanu. (2021). About the Free and Forced Nutation: The Daily Nutation. American Journal of Astronomy and Astrophysics, 9(2), 18-21. https://doi.org/10.11648/j.ajaa.20210902.12

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ACS Style

Monica Zoe Ciobanu. About the Free and Forced Nutation: The Daily Nutation. Am. J. Astron. Astrophys. 2021, 9(2), 18-21. doi: 10.11648/j.ajaa.20210902.12

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AMA Style

Monica Zoe Ciobanu. About the Free and Forced Nutation: The Daily Nutation. Am J Astron Astrophys. 2021;9(2):18-21. doi: 10.11648/j.ajaa.20210902.12

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@article{10.11648/j.ajaa.20210902.12,
  author = {Monica Zoe Ciobanu},
  title = {About the Free and Forced Nutation: The Daily Nutation},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {2},
  pages = {18-21},
  doi = {10.11648/j.ajaa.20210902.12},
  url = {https://doi.org/10.11648/j.ajaa.20210902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210902.12},
  abstract = {To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - About the Free and Forced Nutation: The Daily Nutation
AU  - Monica Zoe Ciobanu
Y1  - 2021/05/08
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210902.12
DO  - 10.11648/j.ajaa.20210902.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 18
EP  - 21
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210902.12
AB  - To explain the nutation phenomenon, Euler chose a geocentric frame of coordinates to present his dynamical equations. In accordance with his formulas, the nutation is caused by a momentum relative to the Earth's center, due to certain external forces. Further, Poinsot presented a special case of the Euler's equations, when any momentum of those certain external forces does not exist. Due to a problematic approximation, Poinsot announced that in this case may take place a nutation period of 10 month, named “free period”, to distinguish it from the Euler's dynamical solution, known as “forced nutation”. After Poinsot, the notion of “free nutation” was extended also to those nutation phenomena which have only a geophysical origin, without a momentum of certain external forces. Usually, the daily nutation is considered as being a free nutation phenomenon. In order to search for a forced daily nutation component, the daily trajectory of the Earth-Moon barycenter inside the Earth is used (a simple scheme of this barycenter trajectory is presented in a geocentric system of axes). Finally, if the ecliptic line is accepted to be described by the Earth-Moon barycenter, it must be accepted, too, that a torque due the Sun and the Moon acts during a sideral day interval on diurnal Earth rotation around its axis. Due to the small value of the nutation constant, a period of 18,6 years is needed to correctly and completely detect the forced daily nutation; this phenomenon permanently presents very fine variations depending on the longitude of the ascending lunar node, the Moon’s declination and the Sun’s ecliptic longitude.
VL  - 9
IS  - 2
ER  -

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