Optimization of Sphere Population for Electrostatic Multi-Sphere Method

Stevenson, Daan; Schaub, Hanspeter

doi:10.1109/tps.2013.2283716

Cited by 17 publications

(4 citation statements)

References 13 publications

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“…The cylinder shape is representative of many upper stage rocket bodies such as the Centaur, which may experience a tumbling motion that must be removed if any spacecraft wishes to perform a docking maneuver. The 3-sphere MSM charge distribution presented in Stevenson and Schaub (2013b) for the cylinder in Fig. 2, at separation distances considered by this survey, agrees on the order of 1% with commercial finite element analysis (FEA) software: Maxwell 3D.…”

Section: Electrostatic Force and Torque Modelingsupporting

confidence: 65%

Prospects and challenges of touchless electrostatic detumbling of small bodies

Bennett

Stevenson

Hogan

et al. 2015

Advances in Space Research

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Section: Electrostatic Force and Torque Modelingsupporting

confidence: 65%

Prospects and challenges of touchless electrostatic detumbling of small bodies

Bennett

Stevenson

Hogan

et al. 2015

Advances in Space Research

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“…Specifically, this reference provides detailed analysis of the interaction between a charged cylinder and a sphere, and this system will be used to study the de-spin control concepts that are the basis of this manuscript. While it is possible to capture the induced charge effects that occur with very close proximity scenarios with a larger set of spheres distributed on the surface of the objects [21], the 3D effects that result in torques exerted on the cylinder at larger separation distances are sufficiently captured when three spheres are used in the cylinder model. While the voltage of the three spheres representing the cylinder are held at the same potential, the resulting approximated charge distribution will be non-homogeneous.…”

Section: Multi-sphere Methodsmentioning

confidence: 99%

“…A recently proposed electrostatic force modeling technique, called the MultiSphere Method (MSM) is able to provide a reduced order model suitable for faster-than-realtime dynamic simulations [20,21]. Both bodies are assumed to have a conducting outer surface, such that constant surface potential is maintained with active charge emission.…”

Section: Introductionmentioning

confidence: 99%

Prospects of Relative Attitude Control Using Coulomb Actuation

Schaub

Stevenson

2013

J of Astronaut Sci

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The relative attitude is studied between two charge controlled spacecraft being held at a fixed separation distance. While one body has a spherical shape, the 2nd body is assumed to be non-spherical and tumbling. The attitude control goal is to arrest the rotation of the 2nd body. While prior work has identified the existence of torques between charged bodies, this is the first analytical study on a charged feedback attitude control. Using the recently developed multi-sphere method to provide a simplified electrostatic force and torque model between non-spherical shapes, Lyapunov theory is used to develop a stabilizing attitude control using spacecraft potential as the control variable. Zero and non-zero equilibrium potentials are considered, with the later suitable for the electrostatic tug concept. With a pulling configuration, the cylinder will come to rest with the long axis aligned with the inter-vehicle axis in a stable configuration. For a pusher, the cylinder will settle 90 degrees rotated from this axis. Numerical simulations illustrate the control performance.

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“…Using an elastance‐based formulation, the voltage at every node V is given by

V = [S] Q

where [ S ] is the elastance matrix and Q is the charge on each node. There are many ways to make [ S ], including the Method of Moments (Gibson, ) and the Surface Multi‐Sphere Method (Stevenson & Schaub, ). In this work Method of Moments is used, which gives the elements of [ S ] for two parallel plates perpendicular to the z axis to be

S_{i, j} = \int_{- Δy / 2}^{Δy / 2} \int_{- Δx / 2}^{Δx / 2} \frac{normald x^{'} normald y^{'}}{\sqrt{{(x_{c} + x^{'})}^{2} + {(y_{c} + y^{'})}^{2} + z_{c}^{2}}}

where x c , y c are the center‐to‐center x and y displacements for the two area elements i and j and z c is the displacement in the z direction.…”

Section: Propagation Modelmentioning

confidence: 99%

Space Weather Influence on Electromagnetic Geosynchronous Debris Perturbations Using Statistical Fluxes

Hughes

Schaub

2018

Space Weather

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Due to the space plasma and the Sun, spacecraft at geosynchronous Earth orbit can charge naturally negative tens of kV. This charging can cause arcing which can damage spacecraft electronics and solar panels. A charged spacecraft will also experience a perturbative force and torque due to Earth's electric and magnetic fields. These electromagnetic perturbations have recently been postulated to cause significant orbital changes for lightweight debris objects. This paper investigates the effects of electromagnetic perturbations by using a charging model that uses measured flux distributions to better simulate natural charging and includes the convection electric field. This is done for a calm space weather case of KP = 2−, a stormy case where KP = 8, and a worst possible case where the voltage is held at −30 kV the entire time. It is found that neglecting electromagnetic effects on lightweight Mylar debris can lead to 100 km displacements after only a one orbit, and the covariance associated with such objects must be increased during periods of high charging.

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Optimization of Sphere Population for Electrostatic Multi-Sphere Method

Cited by 17 publications

References 13 publications

Prospects and challenges of touchless electrostatic detumbling of small bodies

Prospects and challenges of touchless electrostatic detumbling of small bodies

Prospects of Relative Attitude Control Using Coulomb Actuation

Space Weather Influence on Electromagnetic Geosynchronous Debris Perturbations Using Statistical Fluxes

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