Abstract
Let \(\{\mathcal{M};d\mu \}\)be a rigid system in precession abouta pole O. Introduce a fixed inertial triad Σ and a moving triad S, both with originat O, so that S is in rigid motion with respect to Σ with angular characteristic ω. The latter is the unknown of the motion.The system is acted upon by external forcesthat generate a resultant moment M (e)with respect to the pole O. The constraint that keeps O fixed and other possible constraintsgive rise to reactions of resultant moment \(\mathcal{M}\)with respect to O. It is assumed that the moment M (e) and \(\mathcal{M}\)are known functions of ω, or equivalently of the Euler angles.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Prove that this is the only admissible solution of g(θ) = 0 for all a ≥ 0. Prove also that f(θ) < 0 for θ > θ1.
- 2.
For an asymptotic analysis as ω o, 3 → ∞ see §10c of the Complements.
- 3.
From Latin equi noctis, since when the Sun is in that position, day and night have the same duration.
- 4.
Observed first by Hipparchus of Nicaea, (circa 190–126 BCE).Hipparchus had compiled a map of the sky including about 800 stars along with their coordinates and their relative brightness. Comparing his map with the one compiled by Timocharis of Alexandria about 50 years earlier,he noticed a difference of about 2∘ in the position of the same stars. He explained the difference by the precession of equinoxes, whoseadvance he estimated to be about 36 seconds. Modern calculations have it at about 50 seconds. Hipparchus’s map remained essentially unchanged up to the fifteenth century, except for the addition of new stars by Ptolemy (second century CE). Generations of astronomers based their investigations on that map, including Copernicus (1473–1543) and Galileo (1564–1642).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
DiBenedetto, E. (2011). Precessions and Gyroscopes. In: Classical Mechanics. Cornerstones. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4648-6_7
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4648-6_7
Published:
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4526-7
Online ISBN: 978-0-8176-4648-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)