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Particle Mechanics Read chapter Read first chapter

2013 | OriginalPaper | Chapter

2. Rigid Body Mechanics

Author : Roger F. Gans

Published in: Engineering Dynamics

Publisher: Springer New York

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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…

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previous chapter Particle Mechanics
next chapter Forces and Constraints
Footnotes
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.
 
Literature
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
Metadata
Title
Rigid Body Mechanics
Author
Roger F. Gans
Copyright Year
2013
Publisher
Springer New York
Book
Engineering Dynamics

Print ISBN: 978-1-4614-3929-5

Electronic ISBN: 978-1-4614-3930-1

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-3930-1_2

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