Content deleted Content added
rm Youtube links, not WP:RS Tags: Mobile edit Mobile web edit Advanced mobile edit |
46.242.8.153 (talk) Undid revision 920272182 by MarkH21 (talk) Vandalism Tag: Undo |
||
Line 5: | Line 5: | ||
where <math>E</math> is the energy and <math>x,y,z</math> are the components of the [[angular momentum]], given in body's principal reference frame, with corresponding [[moment of inertia|principal moments of inertia]] <math>A,B,C</math>. The construction of such [[Ellipsoid#Applications|ellipsoid]] was conceived by [[James MacCullagh]].<ref>On the Rotation of a Solid Body round a Fixed Point; being an account of the late Professor Mac Cullagh's Lectures on that subject. Compiled by the Rev. Samuel Haughton, Fellow of Trinity College, Dublin. [Transactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849.]</ref> |
where <math>E</math> is the energy and <math>x,y,z</math> are the components of the [[angular momentum]], given in body's principal reference frame, with corresponding [[moment of inertia|principal moments of inertia]] <math>A,B,C</math>. The construction of such [[Ellipsoid#Applications|ellipsoid]] was conceived by [[James MacCullagh]].<ref>On the Rotation of a Solid Body round a Fixed Point; being an account of the late Professor Mac Cullagh's Lectures on that subject. Compiled by the Rev. Samuel Haughton, Fellow of Trinity College, Dublin. [Transactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849.]</ref> |
||
An axis, orthogonal to the circular sections of MacCullagh ellipsoid is called '''Galois axis'''.<ref>{{cite article|author=[[Semjon Adlaj|Adlaj S.]]|title=Torque free motion of a rigid body: from Feynman wobbling plate to Dzhanibekov flipping wingnut|url=http://www.ccas.ru/depart/mechanics/TUMUS/Adlaj/FRBM.pdf|date=2017|issn=}}</ref><ref>{{cite journal|author=Adlaj S. Berestova S. Misura N. [[:ru:Митюшов, Евгений Александрович|Mityushov E.]]|title= Illustrations of Rigid Body Motion Along a Separatrix in the Case of Euler-Poinsot|journal=Computer Tools in Science and Education|volume= |issue=2|date=2018|url=http://ipo.spb.ru/journal/article/2025/|pages=05–13|issn=|accessdate=2018-10-30}}</ref> |
An axis, orthogonal to the circular sections of MacCullagh ellipsoid is called '''Galois axis'''.<ref>{{Cite web|url=https://www.youtube.com/watch?v=qjq44LE3iaQ|title=Эффект Джанибекова: точная постановка и аналитическое решение|author=Семинар по механике космического полёта в [[МГУ]] под руководством [[:ru:Сазонов, Виктор Васильевич|Сазонова В.В.]]{{comment|Galois axis is discussed on the 31-st and 32-nd minute}}|date=October 26, 2016|publisher=YouTube|language =russian|accessdate=2018-10-31}}</ref><ref>{{cite article|author=[[Semjon Adlaj|Adlaj S.]]|title=Torque free motion of a rigid body: from Feynman wobbling plate to Dzhanibekov flipping wingnut|url=http://www.ccas.ru/depart/mechanics/TUMUS/Adlaj/FRBM.pdf|date=2017|issn=}}</ref><ref>{{cite journal|author=Adlaj S. Berestova S. Misura N. [[:ru:Митюшов, Евгений Александрович|Mityushov E.]]|title= Illustrations of Rigid Body Motion Along a Separatrix in the Case of Euler-Poinsot|journal=Computer Tools in Science and Education|volume= |issue=2|date=2018|url=http://ipo.spb.ru/journal/article/2025/|pages=05–13|issn=|accessdate=2018-10-30}}</ref> [[Galois]] axis is remarkable for rotating uniformly throughout the critical [[Euler's equations (rigid body dynamics)#Torque-free solutions|torque free motion of a rigid body]], regardless of whether the body [[Tennis racket theorem|“flips”]] or maintains permanent rotation.<ref>{{Cite web|url=https://www.youtube.com/playlist?list=PLvKkSzWgY7KUUSYDqHVdv0mst4nBnLe64|title=An animation of the critical motion of Dzhanibekov's wingnut|publisher=YouTube|language=|accessdate=2018-10-30}}</ref> |
||
== See also == |
== See also == |
Revision as of 19:55, 8 October 2019
The MacCullagh ellipsoid is defined by the equation:
where is the energy and are the components of the angular momentum, given in body's principal reference frame, with corresponding principal moments of inertia . The construction of such ellipsoid was conceived by James MacCullagh.[1]
An axis, orthogonal to the circular sections of MacCullagh ellipsoid is called Galois axis.[2][3][4] Galois axis is remarkable for rotating uniformly throughout the critical torque free motion of a rigid body, regardless of whether the body “flips” or maintains permanent rotation.[5]
See also
References
- ^ On the Rotation of a Solid Body round a Fixed Point; being an account of the late Professor Mac Cullagh's Lectures on that subject. Compiled by the Rev. Samuel Haughton, Fellow of Trinity College, Dublin. [Transactions of the Royal Irish Academy, Vol. xxii. p. 139. Read April 23, 1849.]
- ^ Семинар по механике космического полёта в МГУ под руководством Сазонова В.В.18px|alt= Galois axis is discussed on the 31-st and 32-nd minute (October 26, 2016). "Эффект Джанибекова: точная постановка и аналитическое решение" (in Russian). YouTube. Retrieved 2018-10-31.
{{cite web}}
: Check|author=
value (help)CS1 maint: numeric names: authors list (link) - ^ Template:Cite article
- ^ Adlaj S. Berestova S. Misura N. Mityushov E. (2018). "Illustrations of Rigid Body Motion Along a Separatrix in the Case of Euler-Poinsot". Computer Tools in Science and Education (2): 05–13. Retrieved 2018-10-30.
{{cite journal}}
: Check|author=
value (help) - ^ "An animation of the critical motion of Dzhanibekov's wingnut". YouTube. Retrieved 2018-10-30.