Experimental aspects of the gyroscope’s movement
ABSTRACT: In presence of a uniform gravitational field, Euler equations for a gyroscope can be written as a non-linear equation for the components of Riemann’s stereographic projection of the symmetry axis over a horizontal plane. Under the approximation of nutations with low amplitude, the solution...
- Autores:
-
Morales, P.
Jaramillo Arango, Daniel Esteban
Osorio Vélez, Jaime Alberto
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2016
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/13075
- Acceso en línea:
- http://hdl.handle.net/10495/13075
- Palabra clave:
- Movimiento del giroscopio
Ecuaciones de Euler
- Rights
- openAccess
- License
- Atribución-NoComercial 2.5 Colombia (CC BY-NC 2.5 CO)
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Experimental aspects of the gyroscope’s movement |
| title |
Experimental aspects of the gyroscope’s movement |
| spellingShingle |
Experimental aspects of the gyroscope’s movement Movimiento del giroscopio Ecuaciones de Euler |
| title_short |
Experimental aspects of the gyroscope’s movement |
| title_full |
Experimental aspects of the gyroscope’s movement |
| title_fullStr |
Experimental aspects of the gyroscope’s movement |
| title_full_unstemmed |
Experimental aspects of the gyroscope’s movement |
| title_sort |
Experimental aspects of the gyroscope’s movement |
| dc.creator.fl_str_mv |
Morales, P. Jaramillo Arango, Daniel Esteban Osorio Vélez, Jaime Alberto |
| dc.contributor.author.none.fl_str_mv |
Morales, P. Jaramillo Arango, Daniel Esteban Osorio Vélez, Jaime Alberto |
| dc.subject.none.fl_str_mv |
Movimiento del giroscopio Ecuaciones de Euler |
| topic |
Movimiento del giroscopio Ecuaciones de Euler |
| description |
ABSTRACT: In presence of a uniform gravitational field, Euler equations for a gyroscope can be written as a non-linear equation for the components of Riemann’s stereographic projection of the symmetry axis over a horizontal plane. Under the approximation of nutations with low amplitude, the solution of this equation corresponds to the sum of two rotating vectors with angular frequencies related to both angular velocities of nutation and precession. Such velocities are functions of rotation rapidity and inertia momentum of the gyroscope. From pictures of the movement projection of a commercial gyroscope, and using a laser that turn on during half revolution cycle of a disk, we can determine all kinematic quantities of the gyroscope, velocities of: rotation, precession and nutation, along with the angle of average inclination from axis. After complete a total of 120 experiments, we corroborate that the expressions given for velocities of precession and nutation, in function of rotation, match with experimental data. This is an easy experiment to implement, and can be used in advanced courses of mechanic. |
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2016 |
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2016 |
| dc.date.accessioned.none.fl_str_mv |
2020-01-11T23:03:50Z |
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2020-01-11T23:03:50Z |
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info:eu-repo/semantics/article |
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Artículo de investigación |
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Morales, P., Jaramillo Arango, D. E., & Osorio Vélez, J. A. (2016). Experimental aspects of the gyroscope’s movement. Revista Mexicana de Fisica, (62), 44-50. |
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0035-001X |
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http://hdl.handle.net/10495/13075 |
| identifier_str_mv |
Morales, P., Jaramillo Arango, D. E., & Osorio Vélez, J. A. (2016). Experimental aspects of the gyroscope’s movement. Revista Mexicana de Fisica, (62), 44-50. 0035-001X |
| url |
http://hdl.handle.net/10495/13075 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartofjournalabbrev.spa.fl_str_mv |
Rev. Mex. Fis. |
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Atribución-NoComercial 2.5 Colombia (CC BY-NC 2.5 CO) |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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Sociedad Mexicana de Física |
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Grupo Estado Sólido |
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México |
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Universidad de Antioquia |
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Morales, P.Jaramillo Arango, Daniel EstebanOsorio Vélez, Jaime Alberto2020-01-11T23:03:50Z2020-01-11T23:03:50Z2016Morales, P., Jaramillo Arango, D. E., & Osorio Vélez, J. A. (2016). Experimental aspects of the gyroscope’s movement. Revista Mexicana de Fisica, (62), 44-50.0035-001Xhttp://hdl.handle.net/10495/13075ABSTRACT: In presence of a uniform gravitational field, Euler equations for a gyroscope can be written as a non-linear equation for the components of Riemann’s stereographic projection of the symmetry axis over a horizontal plane. Under the approximation of nutations with low amplitude, the solution of this equation corresponds to the sum of two rotating vectors with angular frequencies related to both angular velocities of nutation and precession. Such velocities are functions of rotation rapidity and inertia momentum of the gyroscope. From pictures of the movement projection of a commercial gyroscope, and using a laser that turn on during half revolution cycle of a disk, we can determine all kinematic quantities of the gyroscope, velocities of: rotation, precession and nutation, along with the angle of average inclination from axis. After complete a total of 120 experiments, we corroborate that the expressions given for velocities of precession and nutation, in function of rotation, match with experimental data. This is an easy experiment to implement, and can be used in advanced courses of mechanic.application/pdfengSociedad Mexicana de FísicaGrupo Estado SólidoMéxicoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85Atribución-NoComercial 2.5 Colombia (CC BY-NC 2.5 CO)info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc/4.0/Movimiento del giroscopioEcuaciones de EulerExperimental aspects of the gyroscope’s movementRev. Mex. Fis.Revista Mexicana de Física44506262CC-LICENSElicense_urllicense_urlArtículo de investigacióntext/plain; charset=utf-849http://bibliotecadigital.udea.edu.co/bitstream/10495/13075/2/license_url4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-80http://bibliotecadigital.udea.edu.co/bitstream/10495/13075/3/license_textd41d8cd98f00b204e9800998ecf8427eMD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-80http://bibliotecadigital.udea.edu.co/bitstream/10495/13075/4/license_rdfd41d8cd98f00b204e9800998ecf8427eMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/13075/5/license.txt8a4605be74aa9ea9d79846c1fba20a33MD55ORIGINALOsorioJaime_2016_ExperimentalAspectsGyroscopes.pdfOsorioJaime_2016_ExperimentalAspectsGyroscopes.pdfArtículo de revistaapplication/pdf1623821http://bibliotecadigital.udea.edu.co/bitstream/10495/13075/1/OsorioJaime_2016_ExperimentalAspectsGyroscopes.pdf17b1608d1d41668e35bc295f0f4bdf25MD5110495/13075oai:bibliotecadigital.udea.edu.co:10495/130752021-05-16 11:49:21.391Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |