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The motion of a body with a plane of symmetry over a three-dimensional sphere under the action of a spherical analogue of Newtonian gravitation

โœ Scribed by A.A. Burov

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
313 KB
Volume
72
Category
Article
ISSN
0021-8928

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โœฆ Synopsis

The problem of the motion of a rigid body possessing a plane of symmetry over the surface of a threedimensional sphere under the action of a spherical analogue of Newtonian gravitation forces is considered. Approaches to introducing spherical analogues of the concepts of centre of mass and centre of gravity are discussed. The spherical analogue of "satellite approach" in the problem of the motion of a rigid body in a central field, which arises on the assumption that the dimensions of the body are small compared with the distance to the gravitating centre, is studied. Within the framework of satellite approach, assuming plane motion of the body, the question of the existence and stability of steady motions is investigated. A spherical analogue of the equation of the plane oscillations of a body in an elliptic orbit is derived.

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โœ A.A. Burov; D.P. Chevallier ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 879 KB

The structure of the forces and moments which arise when a rigid body moves in an unbounded volume of an ideal incompressible fluid under the action of central Newtonian attractive forces is discussed, the equations of motion are written in explicit form, their first integrals are indicated and the