Skip to main content Accessibility help
×
Home

Hamiltonian Structure and Stability Analysis for a Partially Filled Container

  • S. Ahmad (a1) (a2), B. Yue (a2), S. F. Shah (a3) and S. Ahmad (a4)

Abstract

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.

Copyright

Corresponding author

*Corresponding author (salmanbzm@gmail.com)

References

Hide All
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. 32823289 (2009).
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. 558577 (2010).
3. Wu, G. X., “The Sloshing of Stratified Liquid in a Two-Dimensional Rectangular Tank,” Science China Physics, Mechanics & Astronomy, 54, pp. 29 (2011).
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. 14841492 (2009).
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. 435446 (2011).
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. 739746 (2010).
7. Ibrahim, Rauf A., Liquid Sloshing Dynamics, Theory and Applications, Cambridge University Press, (2005).
8. Abzug, M. J., “Fuel Slosh in Skewed Tanks,” Journal of Guidance, Control and Dynamics, 19, pp. 11721177 (1996).
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. 7193 (1987).
10. Tall, I. S., “Time-Invariant Quadratic Hamiltonians Via Generalized Transformations,” American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 02 (2010).
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. 14041409 (1995).
12. Woolsey, C. A., “Reduced Hamiltonian Dynamics for a Rigid Body/Mass Particle System,” Journal of Guidance, Control and Dynamics, 28, pp. 131138 (2005).
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. 130162 (1997).
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. 5460 (1996).
15. Hughes, P. C., Spacecraft Attitude Dynamics, John Wiley & Sons (1986).
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. 160177 (2008).
17. Marsden, J. E. and Ratiu, T. S., Introduction to Mechanics and Symmetry, 2nd Edition, Springer.
18. Hassan, K., Nonlinear Systems, 3rd Edition, Pearson Education, Inc. (2002).
19. Yang, H. Q. and Peupeot, J., “Propellent Sloshing Parameter Extraction from CFD Analysis,” 46th AIAA Joint Propulsion Conference & Exhibit, pp. 2528, Nashville, TN (2010).

Keywords

Related content

Powered by UNSILO

Hamiltonian Structure and Stability Analysis for a Partially Filled Container

  • S. Ahmad (a1) (a2), B. Yue (a2), S. F. Shah (a3) and S. Ahmad (a4)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.