Abstract
In which we find that a rigid body has six degrees of freedom, learn how to describe the orientation of a rigid body in terms of Euler angles, define inertial and body coordinates and find the Euler-Lagrange equations for a single rigid body…
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.
I will address another alternative in Chap. 3.
- 2.
This is only a convention, but it is a very useful one.
- 3.
Note that J* = J 2 in the sense of Eq. 2.17.
- 4.
The full expression in inertial coordinates is much too unwieldy for display.
- 5.
I use the built-in Runge–Kutta method in Mathematica.
- 6.
Spin about the small axis is also stable. I invite the interested reader to verify that numerically.
References
Bedford A, Fowler W (1999) Engineering mechanics dynamics, 2nd edn. Addison-Wesley, Menlo Park
Beer FP, Johnston ER Jr (1988) Vector mechanics for engineers: statics, 5th edn. McGraw-Hill, New York
Goldstein S (1980) Classical mechanics, 2nd edn. Addison-Wesley, Reading
Press WH, Teukolosky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge
Stratton JA (1941) Electromagnetic theory. McGraw-Hill, New York/London
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gans, R.F. (2013). Rigid Body Mechanics. In: Engineering Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3930-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4614-3930-1_2
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3929-5
Online ISBN: 978-1-4614-3930-1
eBook Packages: EngineeringEngineering (R0)