Study on the dynamics, relative equilibria, and stability for liquid-filled spacecraft with flexible appendage

From the Lagrangian side of geometric mechanics, the dynamics, relative equilibria, and stability analysis for a rigid spacecraft coupled with liquid propellant, flexible appendage, and momentum wheel are studied. The liquid propellant nonlinear sloshing is equivalently modeled by a 3D rigid pendulu...

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Bibliographic Details
Published in:Acta mechanica 2022-09, Vol.233 (9), p.3557-3578
Main Authors: Yi, Zhonggui, Yue, Baozeng
Format: Article
Language:English
Subjects:
Aerospace engineering
Analysis
Attitudes
Classical and Continuum Physics
Control
Cylindrical tanks
Dynamic stability
Dynamical Systems
Energy
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Equilibrium
Heat and Mass Transfer
Lie groups
Liquid propellants
Mechanics
Original Paper
Reaction wheels
Rotating liquids
Solid Mechanics
Space ships
Space vehicles
Spacecraft
Spacecraft stability
Spherical tanks
Stability analysis
Theoretical and Applied Mechanics
Vibration
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Summary:From the Lagrangian side of geometric mechanics, the dynamics, relative equilibria, and stability analysis for a rigid spacecraft coupled with liquid propellant, flexible appendage, and momentum wheel are studied. The liquid propellant nonlinear sloshing is equivalently modeled by a 3D rigid pendulum, which can effectively imitate the large-amplitude lateral sloshing accompanied by liquid rotation-starting, rotary sloshing, and spin motion of partially filled liquid in a closed cylindrical or spherical tank. The flexible attachment is modeled as a geometrically exact rod, which can accommodate arbitrarily large deformations in three dimensions, including extension, shear, bending, and twist. The global and coordinate-free dynamical equations are derived from the perspective of Lagrangian geometry. According to the principle of symmetric criticality, the relative equilibria and associated properties are investigated. Finally, in terms of the energy–momentum method and block diagonalization technique, the formal stability conditions for particular relative equilibria of the coupled spacecraft system are obtained.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03269-5