Two-Craft Coulomb-Force Formation Dynamics and Stability Analysis with Debye Length Characteristics

Yamamoto, Utako; Yamakawa, Hiroshi

doi:10.2514/6.2008-7361

Cited by 8 publications

(4 citation statements)

References 3 publications

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“…12 0 (8) shows that an equilibrium exists only in the absence of any momentum exchange. This result corresponds to the well-known leader-follower formation.…”

Section: The Solutionmentioning

confidence: 96%

“…S ATELLITE formations show such promise for enhanced performance of missions in space that researchers are arduously researching relative control using conventional thrusting [1], tethers [2][3][4], Lorentz forces [5], coulomb forces from charged satellites [6][7][8], and the linear impulse from lasers [9][10][11]. Theoretically, all of these stationkeeping approaches except for thrusting can provide some formation control without expenditure of fuel.…”

Section: Introductionmentioning

confidence: 99%

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Static Formations Using Momentum Exchange Between Satellites

Tragesser

2009

Journal of Guidance, Control, and Dynamics

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Feasible operations of satellite formations are dependent upon an efficient way to affect the relative motion. One possible means of formation stationkeeping is for satellites to exchange momentum in the form of radiation or mass. This approach could potentially provide a mutually repulsive force between satellites without the expenditure of propellant. This paper characterizes equilibria positions in the rotating orbital frame for an arbitrary number of satellites subjected to equal and opposite repulsive force between specifiable satellite pairs. Equilibrium configurations are found that allow arbitrary dispersion in the plane perpendicular to nadir. Stability analysis of these equilibria show stable out-of-plane motion and unstable in-plane motion. A strategy is developed to stabilize the system and to reconfigure the formation geometry. Finally, a simulation including Earth oblateness demonstrates the dynamic feasibility of this method of orbit control. Nomenclature d = nominal distance between satellites K D = derivative gain for out-of-plane damping K p = proportional gain for in-plane control m i = mass of ith satellite n = mean motion of the reference orbit R i = position of the ith satellite in an Earth-centered inertial frame r i = position of the ith satellite relative to a circular reference orbit r ij = position of the ith satellite relative to the jth satellite ( r ij r i r j ) u ij = repulsive force between ith and jth satellite ( u ji ) u ix = x component of control acceleration on the ith satellite u iy = y component of control acceleration on the ith satellite x i = radial coordinate for ith satellite x i = equilibrium (nominal) value of radial coordinate for ith satellite y i = along-track coordinate for ith satellite y i = equilibrium (nominal) value of along-track coordinate for ith satellite z i = out-of-plane coordinate for ith satellite z i = equilibrium (nominal) value of out-of-plane coordinate for ith satellite ij = magnitude of the repulsive force between the ith and jth satellite z i = nominal separation distance between the ith and (i 1) th satellites (z i z i z i1 ) x i = radial displacement from equilibrium for ith satellite y i = along-track displacement from equilibrium for ith satellite z i = out-of-plane displacement from equilibrium for ith satellite

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“…12 0 (8) shows that an equilibrium exists only in the absence of any momentum exchange. This result corresponds to the well-known leader-follower formation.…”

Section: The Solutionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Static Formations Using Momentum Exchange Between Satellites

Tragesser

2009

Journal of Guidance, Control, and Dynamics

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“…The concept of formation flying using inter-spacecraft Coulomb force was first introduced by King et al 6 Then several works investigated the dynamics, stability and control of Coulomb spacecraft formations. 7, 8 Pollock et al studied the relative motion which includes the effect of both Lorentz and Coulomb forces and the dominant force are identified. 9 The feasibility of Lorentz-augmented spacecraft remains an open question.…”

Section: Introductionmentioning

confidence: 99%

Spacecraft Relative Dynamics under the Infuluence of Geomagnetic Lorentz Force

Yamakawa

Bando

Yano

et al. 2010

AIAA/AAS Astrodynamics Specialist Conference

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The motion of a charged satellite subjected to the Earth's magnetic field is considered. Lorentz force, which acts on charged particle when it is moving through the magnetic field, provides a new concepts of propellant-less electromagnetic propulsion. We derive a dynamical model of a charged spacecraft including the effect of Lorentz force in the vicinity of circular and elliptic orbit and consider its application to formation flight. Based on Hill-Clohessy-Wiltshire equations and Tschauner-Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on linearized equations in the equatorial case show that the stability of the periodic solutions. Numerical simulations revealed that the periodic solutions which are useful for the formation are obtained for both circular and elliptic reference orbits.The control strategy for the propellantless rendezvous and reconfiguration are developed.

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“…The orbits of a spacecraft that are accelerated by the Lorentz force are termed Lorentz-augmented orbits, because the Lorentz force cannot completely replace traditional rocket propulsion. After Peck (2005), a series of papers (King et al 2003;Natarajan & Schaub 2006;Streetman & Peck 2007;Yamamoto & Yamakawa 2008;Yamakawa et al 2010) applied charge control techniques to utilize Lorentz forces to control the orbit of a satellite.…”

Section: Introductionmentioning

confidence: 99%

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

Abdel‐Aziz¹,

Shoaib²

2014

Res. Astron. Astrophys.

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Attitude Dynamics of a rigid artificial satellite subject to gravity gradient and Lorentz torques in a circular orbit is considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite's surface. We assume that the satellite is moving in Low Earth Orbit (LEO) in the geomagnetic field which is considered as a dipole model. Our model of the torque due to the Lorentz force is developed for a general shape of artificial satellite, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and their existence conditions are obtained. The numerical results show that the charge q and radius ρ 0 of the charged center of satellite provide a certain type of semi passive control for the attitude of satellite. The technique for such kind of control would be to increase or decrease the electrostatic radiation screening of the satellite. The results obtained confirm that the change in charge can effect the magnitude of the Lorentz torque, which may affect the satellite's control. Moreover, the relation between the magnitude of the Lorentz torque and inclination of the orbits is investigated.

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Two-Craft Coulomb-Force Formation Dynamics and Stability Analysis with Debye Length Characteristics

Cited by 8 publications

References 3 publications

Static Formations Using Momentum Exchange Between Satellites

Static Formations Using Momentum Exchange Between Satellites

Spacecraft Relative Dynamics under the Infuluence of Geomagnetic Lorentz Force

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

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