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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, Pakistan Department 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)
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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.

Keywords

Hamiltonian systemFluid sloshingEquivalent mechanical modelAttitude dynamics
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

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