Spatial equilibria of multibody chain in a circular orbit

Guerman, Anna D.

doi:10.1016/j.actaastro.2005.05.002

Cited by 14 publications

(14 citation statements)

References 18 publications

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“…Moreover, the dynamics of the multibody connected system takes its mathematical non-integrability from CR3BP, which is confined in the orbital plane of the mass center in this study for convenience. Therefore, both above assumptions are quite common [15,17,18,20,21].…”

Section: Hamiltonian Dynamics and Its Symmetriesmentioning

confidence: 97%

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Nonlinear Dynamics of a Two-Chain, Three-Body Formation System

Yan

Liu

2012

J of Astronaut Sci

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Multibody formation constitutes a new architecture wherein the functional capabilities of a monolithic satellite are distributed, and some planned missions have begun to take advantage of the benefits offered by the use of satellite formations. The nonlinear dynamics of a two-chain, three-body formation system located on a circular orbit on the Earth is presented in this paper with the assist of nonlinear theory in astrodynamics. Different from only five libration points solved from the circular restricted three-body system, there exist sixteen equilibria for the chain system yielded by its geometry of the pseudo-potential function. For some hyperbolic equilibria, an iterative procedure is developed to correct numerically periodic orbits near them, which are referred as Lyapunov orbits in this paper. The invariant manifolds originating from those orbits are employed by Poincaré mapping to create the heteroclinic or homoclinic trajectories, and some non-transversal intersections between them are addressed in this paper.

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Section: Hamiltonian Dynamics and Its Symmetriesmentioning

confidence: 97%

“…Guerman [20] developed an analysis method for the planar multibody system. This method allows the identification of some possible equilibrium configurations of an n-link chain in the orbit plane as well as the determination of their existence conditions; the method was then extended into the spatial case [21].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics of a Two-Chain, Three-Body Formation System

Yan

Liu

2012

J of Astronaut Sci

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“…It should, however, be emphasized that stationary configurations exist, which are not situated in the orbit plane. In [17] these general stationary configurations have been investigated for a chain structure. The present investigation follows the same steps as [9] and is based on the same properties but are extended to the present case of a tree structure, making use of the graph-based parameterisation of the topology.…”

Section: Stationary Configuration In the Orbit Planementioning

confidence: 99%

“…The stationary configurations situated in the orbit plane of an N-body chain were found in [9] through an investigation of the stationary points of the potential energy and an upper limit on total number of stationary points was determined. The investigation was further expanded in [17] to also include the out-of-plane dimension of the configuration space. Another approach to determine stationary configurations of satellite formations was made in [18] where the equations of a stationary configuration were deduced assuming that two satellites of the formation could affect each other by a radial force.…”

Section: Introductionmentioning

confidence: 99%

Modeling of tethered satellite formations using graph theory

2011

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a b s t r a c tTethered satellite formations have recently gained increasing attention due to future mission proposals. Several different formations have been investigated for their dynamic properties and control schemes have been suggested. Formulating the equations of motion and investigation which geometries could form stable formations in space are cumbersome when done at a case to case basis, and a common framework providing a basic model of the dynamics of tethered satellite formations can therefore be advantageous. This paper suggests the use of graph theoretical quantities to describe a tethered satellite formation and proposes a method to deduce the equations of motion for the attitude dynamics of the formation in a compact form. The use of graph theory and Lagrange mechanics together allows a broad class of formations to be described using the same framework. A method is stated for finding stationary configurations and an upper limit of their number is determined. The method is shown to be valid for general tethered satellite formations that form a tree structure.

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“…It is called n-chain. The most general description of this type of systems in an orbital environment was done by Guerman (2003Guerman ( , 2006. Among other things, for such systems certain families of equilibria were found.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of multibody chains in circular orbit: non-integrability of equations of motion

Maciejewski

Przybylska

2016

Celest Mech Dyn Astr

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This paper discusses the dynamics of systems of point masses joined by massless rigid rods in the field of a potential force. The general form of equations of motion for such systems is obtained. The dynamics of a linear chain of mass points moving around a central body in an orbit is analysed. The non-integrability of the chain of three masses moving in a circular Kepler orbit around a central body is proven. This was achieved thanks to an analysis of variational equations along two particular solutions and an investigation of their differential Galois groups.

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Spatial equilibria of multibody chain in a circular orbit

Cited by 14 publications

References 18 publications

Nonlinear Dynamics of a Two-Chain, Three-Body Formation System

Nonlinear Dynamics of a Two-Chain, Three-Body Formation System

Modeling of tethered satellite formations using graph theory

Dynamics of multibody chains in circular orbit: non-integrability of equations of motion

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