Analysis of the applicability of collision probability algorithms for nonlinear relative motion

The relative motion of an outline of the rendezvous problem has been studied by assuming that the chief satellite is in circular symmetric orbits. The legitimacy of perturbation techniques and nonlinear relative motion are investigated. The deputy satellite equations of motion with respect to the fixed references at the center of the chief satellite are nonlinear in the general case. We found the periodic solutions of the linear relative motion satellite and for the nonlinear relative motion satellite using the Lindstedt–Poincaré technique. Comparisons among the analytical solutions of linear and nonlinear motions and the obtained solution by the numerical integration of the explicit Euler method for both motions are investigated. We demonstrate that both analytical and numerical solutions of linear motion are symmetric periodic. However, the solutions of nonlinear motion obtained by the Lindstedt–Poincaré technique are periodic and the numerical solutions obtained by integration by using explicit Euler method are non-periodic. Thus, the Lindstedt–Poincaré technique is recommended for designing the periodic solutions. Furthermore, a comparison between linear and nonlinear analytical solutions of relative motion is investigated graphically.

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Satellite Collision Probability for Non-Linear Relative Motion

AIAA/AAS Astrodynamics Specialist Conference and Exhibit ◽

10.2514/6.2002-4632 ◽

2002 ◽

Cited By ~ 2

Author(s):

Russell Patera

Keyword(s):

Relative Motion ◽

Collision Probability ◽

Non Linear

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The restoration of blurred electron micrographs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100142529 ◽

1986 ◽

Vol 44 ◽

pp. 180-181

Author(s):

Bridget Carragher ◽

David A. Bluemke ◽

Michael J. Potel ◽

Robert Josephs

Keyword(s):

Cross Section ◽

Electron Micrographs ◽

Relative Motion ◽

Finite Thickness ◽

Image Plane ◽

Helical Axis ◽

Thin Sections ◽

Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

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