Euler force

In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration^[1] or transverse acceleration^[2] it is the fictitious tangential force that is felt as a result of any radial acceleration. In other words, 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.^[3] ^[4]

Contents

1 Euler Force Example
2 Euler acceleration
3 Euler force
4 See also
5 Notes and references

Euler Force Example

Main article: Rotating reference frame

For person on 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 the person towards the front of the horse. The euler force is perpendicular to the centrifugal force.

Euler acceleration

Main article: Rotating reference frame

The direction and magnitude of the Euler acceleration is given by:

$\boldsymbol{a}_\mathrm{Euler} = - \frac{d\boldsymbol\omega}{dt} \times \mathbf{r}$

where:

ω is the angular velocity of rotation of the reference frame;

r is the vector position of the point where the acceleration is measured relative to the axis of the rotation.

Euler force

Using the above acceleration, the Euler force is:

$\boldsymbol{F}_\mathrm{Euler} = m \boldsymbol{a}_\mathrm{Euler} = - m \frac{d\boldsymbol\omega}{dt} \times \mathbf{r} \ ,$

where:

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

See also

Notes and references

^ David Morin (2008). Introduction to classical mechanics: with problems and solutions. Cambridge University Press. p. 469. ISBN 0521876222. http://books.google.com/books?id=Ni6CD7K2X4MC&pg=PA469&dq=acceleration+azimuthal+inauthor:Morin&lr=&as_brr=0.
^ Grant R. Fowles and George L. Cassiday (1999). Analytical Mechanics, 6th ed.. Harcourt College Publishers. p. 178.
^ Richard H Battin (1999). An introduction to the mathematics and methods of astrodynamics. Reston, VA: American Institute of Aeronautics and Astronautics. p. p. 102. ISBN 1563473429. 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.
^ Jerrold E. Marsden, Tudor S. Ratiu (1999). Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Springer. p. p. 251. ISBN 038798643X. http://books.google.com/books?id=I2gH9ZIs-3AC&pg=PP1&dq=isbn:038798643X&sig=tDWUiGpvGVpbRCCQcGK0Bx5Yk3g#PPA251,M1.