Evolution equations of translational-rotational motion of a non-stationary triaxial body in a central gravitational field

IF 0.7 Q4 MECHANICS Theoretical and Applied Mechanics Pub Date : 2020-01-01 DOI:10.2298/tam191130007m
M. Minglibayev, A. Prokopenya, O. Baisbayeva
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引用次数: 1

Abstract

. The translational-rotational motion of a triaxial body with constant dynamic shape and variable size and mass in a non-stationary Newtonian central gravitational field is investigated. Differential equations of motion of the triaxial body in the relative coordinate system with the origin at the center of a non-stationary spherical body are obtained. The axes of the Cartesian coordinate system fixed to the non-stationary triaxial body are coincident with its principal axes and their relative orientation is assumed to remain unchanged in the course of evolution. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is obtained. Differential equations of translational-rotational motion of the non-stationary triaxial body are derived in Jacobi osculating variables and are studied with the perturba- tion theory methods. The perturbing function is expanded in power series in terms of the Delaunay–Andoyer elements up to the second harmonic element inclusive. The evolution equations of the translational-rotational motion of the non-stationary triaxial body are obtained in the osculating elements of Delaunay–Andoyer.
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中心引力场中非定常三轴体平移旋转运动的演化方程
. 研究了非稳态牛顿中心引力场中具有恒定动态形状、变尺寸和变质量的三轴物体的平移-旋转运动。得到了以非定常球面为中心的三轴体在相对坐标系中的运动微分方程。固定在非静止三轴体上的笛卡儿坐标系各轴与三轴的主轴重合,并假定它们的相对方位在演化过程中保持不变。得到了变大小变质量的三轴体与变大小变质量的球面体的牛顿相互作用的力函数的解析表达式。推导了非定常三轴体在雅可比接触变量下的平移-旋转运动微分方程,并用摄动理论方法进行了研究。扰动函数以Delaunay-Andoyer元的幂级数展开,直至包含二次谐波元。得到了非定常三轴体在Delaunay-Andoyer耦合单元中平移-旋转运动的演化方程。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
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