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In [[classical mechanics]], the '''Euler acceleration''' (named for [[Leonhard Euler]]), also known as '''azimuthal acceleration'''<ref name=Morin>{{cite book |author=David Morin |url=http://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA469&dq=acceleration+azimuthal+inauthor:Morin&lr=&as_brr=0 |title=Introduction to classical mechanics: with problems and solutions |page= 469 |isbn= 0-521-87622-2 |year=2008 |publisher=Cambridge University Press}}</ref> or '''transverse acceleration''',<ref name=Fowles>{{cite book |author=Grant R. Fowles and George L. Cassiday|title=Analytical Mechanics, 6th ed.|page=178|year=1999|publisher=Harcourt College Publishers}}</ref> is the [[Fictitious force|fictitious]] tangential force that is felt as a result of any radial acceleration. In other words, it is an [[acceleration]] that appears when a non-uniformly [[rotating reference frame]] is used for analysis of motion and there is variation in the [[angular velocity]] of the [[frame of reference|reference frame]]'s axes. This article is restricted to a frame of reference that rotates about a fixed axis. | |||
The '''Euler force''' is a [[fictitious force]] on a body that is related to the Euler acceleration by '''F''' = ''m'''''a''', where '''a''' is the Euler acceleration and ''m'' is the mass of the body.<ref name=Battin>{{cite book |title=An introduction to the mathematics and methods of astrodynamics |page=102 |author= Richard H Battin |url=http://books.google.com/books?id=OjH7aVhiGdcC&pg=PA102&vq=Euler&dq=%22Euler+acceleration%22&lr=&as_brr=0&source=gbs_search_s&sig=ACfU3U0__alj4q5o16OHM8vGvArm0rqMdg | |||
|isbn=1-56347-342-9 |year=1999 |publisher=American Institute of Aeronautics and Astronautics |location=Reston, VA }}</ref><ref>{{cite book |title=Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems |author=Jerrold E. Marsden, Tudor S. Ratiu |isbn=0-387-98643-X |year=1999 |publisher=Springer |page=251 |url=http://books.google.com/books?id=I2gH9ZIs-3AC&pg=PP1&dq=isbn:038798643X&sig=tDWUiGpvGVpbRCCQcGK0Bx5Yk3g#PPA251,M1}}</ref> | |||
== Intuitive example == | |||
The Euler force will be felt by a person riding a [[merry-go-round]]. As the ride starts, the Euler force will be the apparent force pushing the person to the back of the horse, and as the ride comes to a stop, it will be the apparent force pushing the person towards the front of the horse. The Euler force is perpendicular to the [[Centrifugal force (fictitious)|centrifugal force]] and is in the plane of rotation. | |||
== Mathematical description == | |||
{{Main|Rotating reference frame}} | |||
The direction and magnitude of the Euler acceleration is given by: | |||
:<math> | |||
\mathbf{a}_\mathrm{Euler} = - \frac{d\boldsymbol\omega}{dt} \times \mathbf{r}, | |||
</math> | |||
where '''ω''' is the angular velocity of rotation of the reference frame and '''r''' is the vector position of the point where the acceleration is measured relative to the axis of the rotation. The Euler force on an object of mass ''m'' is then | |||
:<math> \mathbf{F}_\mathrm{Euler} = m \mathbf{a}_\mathrm{Euler} = - m \frac{d\boldsymbol\omega}{dt} \times \mathbf{r}.</math> | |||
==See also== | |||
*[[Fictitious force]] | |||
*[[Coriolis effect]] | |||
*[[Centrifugal force]] | |||
*[[Rotating reference frame]] | |||
*[[Angular acceleration]] | |||
==Notes and references== | |||
<references/> | |||
[[Category:Fictitious forces]] | |||
[[Category:Rotation]] | |||
{{classicalmechanics-stub}} | |||
Revision as of 06:39, 5 January 2014
In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration[1] or transverse acceleration,[2] is the fictitious tangential force that is felt as a result of any radial acceleration. In other words, it is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes. This article is restricted to a frame of reference that rotates about a fixed axis.
The Euler force is a fictitious force on a body that is related to the Euler acceleration by F = ma, where a is the Euler acceleration and m is the mass of the body.[3][4]
Intuitive example
The Euler force will be felt by a person riding a merry-go-round. As the ride starts, the Euler force will be the apparent force pushing the person to the back of the horse, and as the ride comes to a stop, it will be the apparent force pushing the person towards the front of the horse. The Euler force is perpendicular to the centrifugal force and is in the plane of rotation.
Mathematical description
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The direction and magnitude of the Euler acceleration is given by:
where ω is the angular velocity of rotation of the reference frame and r is the vector position of the point where the acceleration is measured relative to the axis of the rotation. The Euler force on an object of mass m is then
See also
Notes and references
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534