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Quaternion Equations of Disturbed Motion of an Artificial Earth Satellite

机译：人工地球卫星干扰运动的四元流方程

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摘要

The quaternion equations of disturbed motion of an artificial Earth satellite (AES) in Earth's gravitational field (with regard to its zonal, tesseral, and sectorial harmonics) are obtained in four-dimensional Kustaanheimo-Stiefel variables and in modified four-dimensional variables. In the latter variables the equations of satellite motion have a simpler and more symmetric structure, as compared to the equations of motion in the Kustaanheimo-Stiefel variables. The obtained equations are linear for undisturbed Keplerian motion and, in general, have the form of equations of motion of a disturbed four-dimensional oscillator. These equations, in contrast to classical equations, are regular (they do not contain specific points of singularity) for satellite motion in the central gravitational field of Earth under an effect of disturbing forces, the description of which does not contain negative, higher-than-first powers of the satellite distance to Earth's center. In these equations, the basic variables are Kustaanheimo-Stiefel variables, or modified four-dimensional variables proposed by the author, as well as satellite motion energy and time. The new independent variable is associated with time by the differential relation containing the satellite distance to Earth's center of mass. The equations are convenient for applying nonlinear mechanics methods and for high-precision numerical calculations. In the case of artificial satellite motion in Earth's gravitational field, the description of which does not take into account the tesseral and sectorial harmonics, but takes into account its zonal harmonics, the first integrals of the equations of satellite motion are found, and the replacements of variables and transformations of these equations are proposed, which allowed one to get, for studying satellite motion, closed systems of differential equations of lower dimension, in particular, the system of equations of fourth and third orders.
机译：地球引力场中的人造地球卫星（AES）的季节方程（关于其区域，胸部和郊区谐波）是在四维kustaan​​heimo-stiemel变量和修改的四维变量中获得的。在后一种变量中，与Kustaan​​heimo-Stiefel变量中的运动方程相比，卫星运动的方程具有更简单和更对称的结构。所获得的方程是用于未受干扰的开绒运动的线性，并且通常具有扰动的四维振荡器的运动方程形式。与经典方程相比，这些方程是常规（它们不包含特定的奇点点）在令人不安的力的效果下，在地球的中央重力场中的卫星运动，其描述不包含负，高于 - 卫星距离与地球中心的距离。在这些等式中，基本变量是Kustaan​​heimo-stiefel变量，或由作者提出的修改四维变量，以及卫星运动能量和时间。新的独立变量与包含与地球骨骼中心的卫星距离的差异关系相关联。方程式便于应用非线性力学方法和高精度数值计算。在地球的引力场中的人造卫星运动的情况下，对其的描述不考虑旋转性和扇形谐波，而是考虑到其区间谐波，找到了卫星运动方程的第一积分，以及替代品提出了这些方程的变量和变换，该方程允许获得，用于研究卫星运动，卫星运动，尤其是第四和第三订单等方程式的系统。

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    《Cosmic research》 |2019年第2期|101-114|共14页
  • 作者

    Chelnokov Yu. N.;

  • 作者单位

    Russian Acad Sci Inst Problems Precise Mech & Control Saratov 410026 Russia;

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