Evolution of the rotational motion of a viscoelastic sphere in a central Newtonian force field

Vilke, V. G.; Kopylov, Stanislav; Markov, Yu. G.

doi:10.1016/0021-8928(85)90122-4

Cited by 8 publications

(2 citation statements)

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“…We shall assume that the values (dui/t3x 9 (i,j = 1, 2, 3) are small (l~ud~x~l << 1) and the deformed state of the sphere is described by the classical theory of the elasticity of small deformations [3]; p = const is the density of the sphere. The transition from the Kening system of the coordinates C~'1¢~ to the orbital axes Cx~yiz~ is given by the sequence of rotations where g~ (i = 1, 2) is the angle between the radius vector R~ and the positive direction of the axis Ox; I is the angle between the perpendicular to the plane, passing through the points M~, M2, C and the axis 043.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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On the motion around the centre of mass of a viscously elastic sphere in the restricted elliptic three-body problem

Demin

Markov

Minyaev

1991

Celestial Mech Dyn Astr

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Al~traet. In the restricted three-body problem we consider the motion of a viscously elastic sphere (planet) with its centre of mass moving in a conditionally-periodic orbit. The approximate equations describing the rotational motion of the sphere in terms of the Andoyer variables are obtained by the method of the separation of motion and averaging; the evolution of the motion is also analysed. Formulation of the ProblemConsider the restricted elliptic problem of three bodies two of which are mass points M 1 and M 2 with masses m, and m2, respectively, which are moving one relative to the other in an elliptic orbit with the radius ofwhere a, e and ~ are the major semiaxis, eccentricity and true anomaly of the orbit, respectively, and the third body M is a passively gravitating deformed sphere. In the inertial system of coordinates O~1~2~3, in which the point O is the barycentre of the two attracting points M, and M2, the axis O~3 is perpendicular to the plane of the orbit and the axis O~ is the line of apsides of the elliptic motion of the attracting points. The radius vectors of the points M~ and M 2 are (see Figure 1):Here xi is the coordinate of the attracting centre Mi in the rotating coordinate system Oxyz, in which the axis Oz coincides with the axis 0¢3 of the inertial system and the axis Ox passes through the points M 1 and M2; G ° is a unit vector along the axis O~. The angular speed of rotation around the axis Oz is defined by the relation d~ COo(1 + e cos ~ )2 f(ml + m2) dt = (1 --e2) 3/2 ' 032 ----a 3 'where o9 0 is the average speed of revolution of the mass points M, and M2, and f is a gravitational constant.

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Section: Formulation Of the Problemmentioning

confidence: 99%

“…The boundary conditions for the function ul are formulated as follows: a" n = 0 over OR, where a is the stress tensor and n is the normal to the surface of the sphere. The solution of Equation (12) will be found as the sum of three functions by analogy with [3]:…”

Section: Ri X/y 2 + Zmentioning

confidence: 99%