Euler force

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. Of the three fictitious forces that appear in a rotating reference frame, only the Euler force results from rotation speeding up or slowing down.

Mathematical description

Main article: Rotating reference frame

The direction and magnitude of the Euler acceleration is given, in the rotating reference frame, by: : \mathbf{a}_\mathrm{Euler} = - \frac{d\boldsymbol\omega}{dt} \times \mathbf{r},

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 in the rotating reference frame is then

: \mathbf{F}\mathrm{Euler} = m \mathbf{a}\mathrm{Euler} = - m \frac{d\boldsymbol\omega}{dt} \times \mathbf{r}.

References

1. Jerrold E. Marsden, Tudor S. Ratiu. (1999). "Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems". Springer.
2. David Morin. (2008). "Introduction to classical mechanics: with problems and solutions". Cambridge University Press.
3. Grant R. Fowles and George L. Cassiday. (1999). "Analytical Mechanics, 6th ed.". Harcourt College Publishers.