Hamiltonian mechanics and relative equilibria of orbiting gyrostats

Hall, Christopher D.; Beck, Jeff

doi:10.1007/bf03256514

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…It is therefore included explicitly in the dynamical model 23 NGravity Gradient = 3p-r X I l r (5) where is the Euclidean norm, p = GM is the Earth's gravitational constant, and r is the position vector from the center of mass of the Earth to the satellite's center of mass expressed in the orbital frame (defined by a right-handed orthogonal set of axes with its z-axis in the nadir direction and its y-axis in the orbit anti-normal direction). Note that these equations derive from a noncanonical Hamiltonian system that is a Lie-Poisson system with skew-symmetric structure matrix J(x):…”

Section: Equations Of Motionmentioning

confidence: 99%

Nonlinear Symplectic Attitude Estimation for Small Satellites

Valpiani

Palmer

2006

AIAA/AAS Astrodynamics Specialist Conference and Exhibit

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Public reporting burden for this collection ot rntormation is estimated to average 1 hour per response, including the time tor reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AUTHOR(S)1ST LT VALPIANI JAMES M A novel method for efficient high-accuracy satellite attitude estimation is presented to address the increasing performance requirements of resource-constrained small satellites. Symplectic numerical methods are applied to the nonlinear estimation problem for Hamiltonian systems, leading to a new general solution that exactly preserves state probability density functions and conserves invariant properties of the dynamics when solving for the state estimate. This nonlinear Symplectic Filter is applied to a standard small satellite mission and simulation results demonstrate orders of magnitude improvement in state and constants of motion estimation when compared to extended and iterative Kalman methods, particularly in the presence of nonlinear dynamics and high accuracy attitude observations. Based on numerous simulations, the authors conclude that this new method shows promise for improved attitude estimation onboard high performance, resource-constrained small satellites. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES

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Section: Equations Of Motionmentioning

confidence: 99%

Nonlinear Symplectic Attitude Estimation for Small Satellites

Valpiani

Palmer

2006

AIAA/AAS Astrodynamics Specialist Conference and Exhibit

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“…In that scope, we first extend the Lagrangian formalism described in (Poincaré, 1901) to a noncanonical Hamiltonian formalism allowing to study relative equilibria in a very efficient manner as in (Maddocks, 1991;Beck and Hall, 1998). The method has proven its efficiency in the context of a rigid satellite in circular orbit (Beck and Hall, 1998), in the analysis of the two rigid body problem (Maciejewski, 1995), and in several studies of the attitude of a satellite with a gyrostat (e.g., Hall and Beck, 2007;Wang and Xu, 2012, and references therein). The approach is described in Sect.…”

Section: Introductionmentioning

confidence: 99%

Rotation of a rigid satellite with a fluid component: a new light onto Titan’s obliquity

Boué

Rambaux

Richard

2017

Celest Mech Dyn Astr

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International audienceWe revisit the rotation dynamics of a rigid satellite with either a liquid core or a global sub-surface ocean. In both problems, the flow of the fluid component is assumed inviscid. The study of a hollow satellite with a liquid core is based on the Poincaré-Hough model which provides exact equations of motion. We introduce an approximation when the ellipticity of the cavity is low. This simplification allows to model both types of satellite in the same manner. The analysis of their rotation is done in a non-canonical Hamiltonian formalism closely related to Poincaré's " forme nouvelle deséquationsdeséquations de la mécanique ". In the case of a satellite with a global ocean, we obtain a seven-degree of freedom system. Six of them account for the motion of the two rigid components, and the last one is associated with the fluid layer. We apply our model to Titan for which the origin of the obliquity is still a debated question. We show that the observed value is compatible with Titan slightly departing from the hydrostatic equilibrium and being in a Cassini equilibrium state

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Hamiltonian structures of dynamics of a gyrostat in a gravitational field

2012

Nonlinear Dyn

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Hamiltonian mechanics and relative equilibria of orbiting gyrostats

Cited by 3 publications

References 14 publications

Nonlinear Symplectic Attitude Estimation for Small Satellites

Nonlinear Symplectic Attitude Estimation for Small Satellites

Rotation of a rigid satellite with a fluid component: a new light onto Titan’s obliquity

Hamiltonian structures of dynamics of a gyrostat in a gravitational field

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