Abstract
Given a specific set of Euler angles, it is common to ask what representations conservative moments and constraint moments possess. In this paper, we discuss the role that a non-orthogonal basis, which we call the dual Euler basis, plays in the representations. The use of the basis is illustrated with applications to potential energies, constraints, and Lagrange’s equations of motion.
Issue Section:
Technical Papers
References
1.
O’Reilly
, O.
M.
, and Srinivasa
,
A. R.
, 2002,
“On Potential Energies and Constraints in the Dynamics of
Rigid Bodies and Particles
,” Math. Probl.
Eng.
1024-123X, 8
(3
), pp.
169
–180
.2.
Rao
, A.
V.
, 2006,
Dynamics of Particles and Rigid Bodies: A Systematic
Approach
, Cambridge University
Press
,
Cambridge
.3.
Antman
, S.
S.
, 1972,
“Solution to Problem 71-24: “Angular Velocity and Moment
Potentials for a Rigid Body,” by J. G. Simmonds
,”
SIAM Rev.
0036-1445, 14
, pp.
649
–652
.4.
Beletskii
, V.
V.
, 1966,
Motion of an Artificial Satellite about its Center of Mass
,
(translated from the Russian by Z.
Lerman)
,
Israel Program for Scientific Translations
,
Jerusalem
.5.
Casey
,
J.
, and
O’Reilly
, O.
M.
, 2006,
“Geometrical Derivation of Lagrange’s Equations for a System
of Rigid Bodies
,” Mathematics and Mechanics of Solids, to
appear.6.
Greenwood
, D.
T.
, 1988,
Classical Dynamics
, 2nd ed.,
Prentice-Hall
, Englewood
Cliffs, NJ
.7.
Casey
,
J.
,
1983, “A Treatment of
Rigid Body Dynamics
,” ASME J. Appl. Mech.
0021-8936, 50
, pp.
905
–907
and Casey
,
J.
,
1983, “A Treatment of
Rigid Body Dynamics
,” ASME J. Appl. Mech.
0021-893651
, p.
227
.8.
Copyright © 2007
by American Society of Mechanical Engineers
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