Euler force

From Wikipedia, the free encyclopedia

 This article needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)

In classical mechanics, the Euler acceleration (named for Leonhard Euler) 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.

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. [1]

[edit] Euler acceleration

Its direction and magnitude is given by:

\boldsymbol{a}_{euler} = - \frac{d\boldsymbol\omega}{dt} \times \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.

[edit] Euler force

\boldsymbol{F}_{euler} = m \boldsymbol{a}_{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.

[edit] Notes and references

  1. ^ Jerrold E. Marsden, Tudor S. Ratiu (1999). Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Springer, p. 251. ISBN 038798643X. 
Areal velocity. This classical mechanics-related article is a stub. You can help Wikipedia by expanding it.
Languages