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首页> 外文会议>International astronautical congress >APPLICATION OF BROUWER-LYDDANE AVERAGING METHOD TO ORBITAL DYNAMICS IN THE GRAVITATIONAL FIELD OF SMALL BODIES
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APPLICATION OF BROUWER-LYDDANE AVERAGING METHOD TO ORBITAL DYNAMICS IN THE GRAVITATIONAL FIELD OF SMALL BODIES

机译：溴二烷平均法在小体引力场轨道动力学中的应用

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The detection on small bodies has been more and more important in modern astronautics because of its unique value in technology and astronomy. The analysis on the orbital dynamics in the near-regime gravitational field of small bodies is a great challenge. However, traditional method usually can not provide analytic solutions of the orbit. In this paper, Hamiltonian mechanics method which Brouwer used in the orbit around the earth is the main tool which is usually used in the gravitation of the earth apart from the traditional method which is to solve differential equations established by spatial coordinates through celestial mechanics. Due to the unique properties of the small body such as its small mass, irregular shape and complicated self-rotation, the difference is that the tesseral harmonics is the main influence besides the zonal harmonics which are generally ignored in the earth. Since this paper aims to study the orbit perturbation around the small body, spherical harmonics model is used to simulate the gravitation of the small body. Then we can build the disturbing potential function and Hamilton's function imitated that in the earth. Then, the detailed steps are taken to study the orbital dynamics. Firstly, establish Lagrange orbit dynamic formulas and change them into Hamilton's canonical equations by replacing orbit elements with Delaunay variables. Then, two variable Canonical transformations based on the lie series are used to eliminate angle variables 1 and g separately in order to reduce the order of Hamilton's function. Finally, six variables have been calculated and divided into secular term, long period term and short period term. The analytic solutions of orbital elements can be got which can reveal the properties of orbital dynamics around the small body directly. With the foundation of these calculations, a typical small body is chosen as an example in this paper and the properties about the equilibrium points and frozen orbits of it are analyzed then. At the end of the paper the results are compared with that calculated in traditional method.
机译：小物体的探测由于其在技术和天文学上的独特价值，在现代航天中已变得越来越重要。对小物体近重力场的轨道动力学进行分析是一个巨大的挑战。但是，传统方法通常无法提供轨道的解析解。本文中，布劳威尔（Brouwer）在绕地球运行的轨道上使用的汉密尔顿力学方法是通常用于地球引力的主要工具，而传统方法则是通过天体力学解决由空间坐标建立的微分方程。由于小物体的独特特性，例如其小巧的质量，不规则的形状和复杂的自转，其区别在于，地带谐波是主要的影响因素，而地带谐波在地球上通常被忽略。由于本文旨在研究小物体周围的轨道扰动，因此使用球谐模型来模拟小物体的引力。然后我们可以建立扰动势函数，而汉密尔顿函数则模拟了地球上的扰动势函数。然后，采取详细步骤来研究轨道动力学。首先，建立拉格朗日轨道动力学公式，并通过用Delaunay变量替换轨道元素，将其转换为汉密尔顿正则方程。然后，使用两个基于lie级数的变量Canonical变换分别消除角度变量1和g，以降低汉密尔顿函数的阶数。最后，计算了六个变量并将其分为长期项，长期项和短期项。可以得到轨道元素的解析解，可以直接揭示小物体周围的轨道动力学特性。在这些计算的基础上，本文以一个典型的小物体为例，然后对其平衡点和冻结轨道的性质进行了分析。最后，将结果与传统方法计算的结果进行了比较。

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