In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration[1] or transverse acceleration[2] 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]
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Euler acceleration
The direction and magnitude of the Euler acceleration is given by:
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:
where:
- m is the mass of the object upon which this fictitious force is exerted.
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.
See also
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