A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

Issue Section:
Technical Papers
Keywords:
kinematics, momentum, matrix algebra
Topics:
Dynamics (Mechanics), Kinematics, Modeling, Momentum, Potential energy, Rotation, Angular momentum
1.
Baruh, Haim, 1999, ANALYTICAL DYNAMICS, McGraw Hill, New York.
2.
Chang
,
C. O.
,
Chou
,
C. S.
, and
Wang
,
S. Z.
,
1991
,
Design of a Viscous ring Nutation Damper for a Freely Precessing Body
,
J. Guid. Control Dyn.
,
14
, pp.
1136
–
1144
.
3.
Thompson, W. T., 1961, INTRODUCTION TO SPACE DYNAMICS, John Wiley and Sons, New York.
4.
Ginsberg, J. H., 1988, ADVANCED ENGINEERING DYNAMICS, Harper and Row, New York.
5.
Goldstein, Herbert, 1965, CLASSICAL MECHANICS, Addison-Wesley Publishing Company, New York.
6.
Rapaport
,
D. C.
,
1985
,
Molecular Dynamics Simulation Using Quaternions
,
J. Comput. Phys.
,
41
, pp.
306
–
314
.
7.
Greenwood, Donald T., 1988, PRINCIPLES OF DYNAMICS, Prentice Hall, Englewood Cliffs, New Jersey.
8.
Nitschke
,
M.
, and
Knickmeyer
,
E. H.
,
2000
,
Rotation Parameters-A Survey of Techniques
,
J. Surv. Eng.
,
126
, pp.
83
–
105
.
9.
Shuster
,
M. D.
,
1993
,
A Survey of Attitude Representations
,
Journal of Astronautical Sciences
,
41
, pp.
531
–
543
.
10.
Spring, K. W., 1986, Euler Parameters and the Use of Quaternion Algebra in the Manipulation of Finite Rotations: A Review, Mechanism and Machine Theory, 21, pp. 365–373.
11.
Nikravesh
,
P. E.
, and
Chung
,
I. S.
,
1982
,
Application of Euler Parameters to the Dynamic Analysis of Three Dimensional Constrained Mechanical Systems
,
J. Mech. Des.
,
104
, pp.
785
–
791
.
12.
Nikravesh
,
P. E.
,
Wehage
,
R. A.
, and
Kwon
,
O. K.
,
1985
,
Euler Parameters in Computational Kinematics and Dynamics: Part 1
,
Journal of Mechanisms, Transmissions and Automation Design
,
107
, pp.
358
–
365
.
13.
Nikravesh
,
P. E.
,
Kwon
,
O. K.
, and
Wehage
,
R. A.
,
1985
,
Euler Parameters in Computational Kinematics and Dynamics: Part 2
,
Journal of Mechanisms, Transmissions and Automation Design
,
107
, pp.
366
–
369
.
14.
Nikravesh, P. E., 1988, COMPUTER AIDED ANALYSIS OF MECHANICAL SYSTEMS, Prentice Hall, Englewood Cliffs, New Jersey.
15.
Vadali
,
S. R.
,
1988
,
On the Euler Parameter Constraint
,
J. Astronaut. Sci.
36
, pp.
259
–
265
.
16.
Morton
, Jr.,
S. Harold
,
1993
,
Hamiltonian and Lagrangian Formulations of Rigid Body Rotational Dynamics Based on Euler Parameters
,
J. Astronaut. Sci.
,
41
, pp.
561
–
5991
.
17.
Simo
,
J. C.
, and
Wong
,
K. K.
,
1991
,
Unconditionally Stable Algorithms for Rigid Body Dynamics That Exactly Preserve Energy and Momentum
,
International Journal of Numerical Methods in Engineering
,
31
, pp.
19
–
52
.
Copyright © 2004
 by ASME
You do not currently have access to this content.