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Hamiltonian Structure and Stability Analysis for a Partially Filled Container

Published online by Cambridge University Press:  16 October 2012

S. Ahmad,
B. Yue,
S. F. Shah and
S. Ahmad
S. Ahmad*
Affiliation:
Department of Humanities & Sciences, Institute of Space Technology, Islamabad 44000, PakistanDepartment of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
B. Yue*
Affiliation:
Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
S. F. Shah
Affiliation:
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
S. Ahmad*
Affiliation:
Department of Mathematics (CASPAM), Bahauddin Zakarya University, Multan 60000, Pakistan
*
*Corresponding author (salmanbzm@gmail.com)
*Corresponding author (salmanbzm@gmail.com)
*Corresponding author (salmanbzm@gmail.com)

Abstract

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Hamiltonian system is a special case of dynamical system. Mostly it is used for potential shaping of mechanical systems stabilization. In our present work, we are using Hamiltonian dynamics to study and control the fuel slosh inside spacecraft tank. Sloshing is the phenomenon which is related with the movement of fluid inside a container in micro and macro scale as well. Sloshing of fluid occurs whenever the frequency of container movement matches with the natural frequency of fluid inside the container. Such type of synchronization may cause the structural damage or could be a reason of moving object's attitude disturbance. In spacecraft technology, the equivalent mechanical model for sloshing is common to use for the representation of fuel slosh. This mechanical model may contain a model of pendulum or a mass attached with a spring. In this article, we are using mass-spring mechanical model coupled with rigid body to derive the equations for Hamiltonian system. Casimir functions are used for proposed model. Conditions for the stability and instability of moving mass are derived using Lyapunov function along with Casimir functions. Simulation work is presented to strengthen the derived results and to distribute the stable and unstable regions graphically.

Keywords

Hamiltonian systemFluid sloshingEquivalent mechanical modelAttitude dynamics

Information

Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013, pp. 79 - 83
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

References

REFERENCES

1. Hong, W., Liu, Z. and Suo, Z., “Inhomogeneous Swelling of a Gel in Equilibrium with a Solvent and Mechanical Load,” International Journal of Solids and Structures, 46, pp. 3282–3289 (2009).Google Scholar
2. Hong, W., Zhao, X. H. and Suo, Z. G., “Deformation and Electrochemistry of Polyelectrolyte Gels,” Journal of Mechanics and Physics of Solids, 58, pp. 558–577 (2010).Google Scholar
3. Wu, G. X., “The Sloshing of Stratified Liquid in a Two-Dimensional Rectangular Tank,” Science China Physics, Mechanics & Astronomy, 54, pp. 2–9 (2011).Google Scholar
4. Yang, W., Liu, S. H. and Lin, H., “Viscous Liquid Sloshing Damping in Cylindrical Container Using a Volume of Fluid Method,” Science in China Series E-Technological Sciences, 52, pp. 1484–1492 (2009).Google Scholar
5. Fu, X. L., Wang, G. F. and Feng, X. Q., “Effects of Surface Elasticity on Mixed-Mode Fracture,” International Journal of Applied Mechanics, 3, pp. 435–446 (2011).Google Scholar
6. Rebouillat, S. and Liksonov, D., “Fluid-Structure Interaction in Partially Filled Liquid Containers: A Comparative Review of Numerical Approaches,” Computer and Fluids, 39, pp. 739–746 (2010).CrossRefGoogle Scholar
7. Ibrahim, Rauf A., Liquid Sloshing Dynamics, Theory and Applications, Cambridge University Press, (2005).Google Scholar
8. Abzug, M. J., “Fuel Slosh in Skewed Tanks,” Journal of Guidance, Control and Dynamics, 19, pp. 1172–1177 (1996).Google Scholar
9. Krishnaprasad, P. S. and Marsden, J. E., “Hamiltonian Structures and Stability for Rigid Bodies with Flexible Attachments,” Archive for Rational Mechanics and Analysis, 98, pp. 71–93 (1987).Google Scholar
10. Tall, I. S., “Time-Invariant Quadratic Hamiltonians Via Generalized Transformations,” American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02 (2010).Google Scholar
11. Chinnery, A. E. and Hall, C. D., “The Motion of a Rigid Body with an Attached Spring-Mass Damper,” Journal of Guidance, Control and Dynamics, 18, pp. 1404–1409 (1995).Google Scholar
12. Woolsey, C. A., “Reduced Hamiltonian Dynamics for a Rigid Body/Mass Particle System,” Journal of Guidance, Control and Dynamics, 28, pp. 131–138 (2005).Google Scholar
13. Leonard, N. E. and Marsden, J. E., “Stability and Drift of Underwater Vehicle Dynamics: Mechanical Systems with Rigid Motion Symmetry,” Physica D, 105, pp. 130–162 (1997).Google Scholar
14. Petsopoulos, T., Regan, F. J. and Barlow, J., “Moving-Mass Roll Control System for Fixed-Trim Re-Entry Vehicle,” Journal of Spacecraft and Rocekts, 33, pp. 54–60 (1996).Google Scholar
15. Hughes, P. C., Spacecraft Attitude Dynamics, John Wiley & Sons (1986).Google Scholar
16. Liu, S. Z. and Trenkler, Gaotz., “Hadamard, Khatri-Rao, Kronecker and Other Matrix Products,” International Journal of Information and Systems Sciences: Computing and Information, 4, pp. 160–177 (2008).Google Scholar
17. Marsden, J. E. and Ratiu, T. S., Introduction to Mechanics and Symmetry, 2nd Edition, Springer.Google Scholar
18. Hassan, K., Nonlinear Systems, 3rd Edition, Pearson Education, Inc. (2002).Google Scholar
19. Yang, H. Q. and Peupeot, J., “Propellent Sloshing Parameter Extraction from CFD Analysis,” 46th AIAA Joint Propulsion Conference & Exhibit, pp. 25–28, Nashville, TN (2010).Google Scholar