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TECHNICAL PAPERS

Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

[+] Author and Article Information
Ravishankar Shivarama, Eric P. Fahrenthold

Department of Mechanical Engineering, University of Texas, Austin, TX 78712

J. Dyn. Sys., Meas., Control 126(1), 124-130 (Apr 12, 2004) (7 pages) doi:10.1115/1.1649977 History: Received August 01, 2002; Revised August 21, 2003; Online April 12, 2004
Copyright © 2004 by ASME
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References

Baruh, Haim, 1999, ANALYTICAL DYNAMICS , McGraw Hill, New York.
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.
Thompson, W. T., 1961, INTRODUCTION TO SPACE DYNAMICS , John Wiley and Sons, New York.
Ginsberg, J. H., 1988, ADVANCED ENGINEERING DYNAMICS , Harper and Row, New York.
Goldstein, Herbert, 1965, CLASSICAL MECHANICS , Addison-Wesley Publishing Company, New York.
Rapaport,  D. C., 1985, Molecular Dynamics Simulation Using Quaternions, J. Comput. Phys., 41, pp. 306–314.
Greenwood, Donald T., 1988, PRINCIPLES OF DYNAMICS , Prentice Hall, Englewood Cliffs, New Jersey.
Nitschke,  M., and Knickmeyer,  E. H., 2000, Rotation Parameters-A Survey of Techniques, J. Surv. Eng., 126, pp. 83–105.
Shuster,  M. D., 1993, A Survey of Attitude Representations, Journal of Astronautical Sciences, 41, pp. 531–543.
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.
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.
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.
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.
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Figures

Grahic Jump Location
First example problem, rotating disk with a translational spring suspension
Grahic Jump Location
First example problem, comparison of Euler angle based and Hamiltonian solutions for the angular momenta versus time; the computed Hamiltonian component hz agrees with the Euler angle solution (diamond symbols) obtained using Eq. (46), while the Hamiltonian components hx and hy are identically zero
Grahic Jump Location
First example problem, numerical solution for the Euler parameters versus time; note that the Euler parameters e1 and e2 are identically zero, and along with the computed solutions for e0 and e3 determine the nonzero Euler angle in accordance with Eq. (2)
Grahic Jump Location
Second example problem, torque free motion of a rigid body, numerical solution for the angular momenta versus time
Grahic Jump Location
Second example problem, torque free motion of a rigid body, numerical solution for the Euler parameters versus time; note that the Euler parameters are continuous functions
Grahic Jump Location
Second example problem, torque free motion of a rigid body, computed Euler angles versus time; note the discontinuities in the Euler angles
Grahic Jump Location
Third example problem, translation and rotation of a spinning top, numerical solution for the normalized components of the angular momentum versus time
Grahic Jump Location
Third example problem, translation and rotation of a spinning top, numerical solution for the center of mass position versus time

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