Open AccessCollision and Stable Regions around Bodies with Simple Geometric Shape
Author(s) -
A. A. Silva,
O. C. Winter,
A. F. B. A. Prado
Publication year - 2009
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2009/396267
Subject(s) - surface (topology) , collision , simple (philosophy) , geometry , point (geometry) , gravitation , impact crater , space (punctuation) , physics , gravitational potential , homogeneous , phase (matter) , point particle , phase space , geometric shape , classical mechanics , mathematical analysis , mathematics , statistical physics , computer science , philosophy , epistemology , quantum mechanics , astronomy , thermodynamics , operating system , computer security
We show the expressions of the gravitational potential of homogeneous bodies with well-defined simple geometric shapes to study the phase space of trajectories around these bodies. The potentials of the rectangular and triangular plates are presented. With these expressions we study the phase space of trajectories of a point of mass around the plates, using the Poincaré surface of section technique. We determined the location and the size of the stable and collision regions in the phase space, and the identification of some resonances. This work is the first and an important step for others studies, considering 3D bodies. The study of the behavior of a point of mass orbiting around these plates (2D), near their corners, can be used as a parameter to understand the influence of the gravitational potential when the particle is close to an irregular surface, such as large craters and ridges
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