# Euler force

In classical mechanics, the **Euler force** is the fictitious tangential force[1]
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 acceleration** (named for Leonhard Euler), also known as **azimuthal acceleration**[2] or **transverse acceleration**[3] is that part of the absolute acceleration that is caused by the variation in the angular velocity of the reference frame.[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. A person on a horse close to the perimeter of the merry-go-round will perceive a greater apparent force than a person on a horse closer to the axis of rotation.

## Mathematical description

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 in the reference frame. The Euler force on an object of mass *m* is then

## See also

## Notes and references

- Jerrold E. Marsden, Tudor S. Ratiu (1999).
*Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems*. Springer. p. 251. ISBN 0-387-98643-X. - David Morin (2008).
*Introduction to classical mechanics: with problems and solutions*. Cambridge University Press. p. 469. ISBN 0-521-87622-2. - 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. 102. ISBN 1-56347-342-9.