Euler force

Euler force

In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal accelerationcite book |author=David Morin |url=http://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA466&dq=Azimuthal+forcel&lr=&as_brr=0&sig=jha8GCqJh5TwRPPbtFfajFrzcKY#PPA469,M1 |title=Introduction to classical mechanics: with problems and solutions |page= p. 469 |isbn= 0521876222 |year=2008 |publisher=Cambridge University Press] 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" = "m" "a", where "a" is the Euler acceleration and "m" is the mass of the body.cite book |title=An introduction to the mathematics and methods of astrodynamics |page=p. 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=1563473429 |year=1999 |publisher=American Institute of Aeronautics and Astronautics |location=Reston, VA ] [cite book |title=Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems |author=Jerrold E. Marsden, Tudor S. Ratiu |isbn=038798643X |year=1999 |publisher=Springer |page=p. 251 |url=http://books.google.com/books?id=I2gH9ZIs-3AC&pg=PP1&dq=isbn:038798643X&sig=tDWUiGpvGVpbRCCQcGK0Bx5Yk3g#PPA251,M1]

Euler acceleration

Its direction and magnitude is given by::oldsymbol{a}_{euler} =- frac{doldsymbolomega}{dt} imes mathbf{r}

where::ω is the angular velocity of the reference frame;:"r" is the radial distance of the point where the acceleration is measured from the axis of the rotation.

Euler force

:oldsymbol{F}_{euler} = m oldsymbol{a}_{euler} =- m frac{doldsymbolomega}{dt} imes mathbf{r}

where::"m" is the mass of the object upon which this fictitious force is exerted.

Notes and references

ee also

*Fictitious force
*Coriolis effect
*Centrifugal force


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