论文标题
使用指数的产品来定义（绘制）轨道等等
Using Products of Exponentials to Define (Draw) Orbits and More
论文作者
论文摘要
指数（POE）公式的乘积是一种数学工具，可在机器人技术中广泛使用。使用指数映射，Lie代数和螺丝理论的优点在于，它允许一种优雅而简洁的方式来描述身体相对于多体系统中另一个身体的方向和位置。尽管POE公式主要用于机器人技术，但该工作旨在证明POE公式作为定义和绘图轨道的替代方法，以给定轨道元素集。这项工作还探讨了轨道力学框架中适应的POE公式的第一个衍生物，该公式允许使用开发的配方从设置的轨道元素中获得卫星状态（位置和速度）。
The Product of Exponentials (PoE) formula is a mathematical tool that is used extensively in robotics. The virtue of using the exponential mapping, Lie Algebra and screw theory is that it allows an elegant and concise way of describing the orientation and position of a body with respect to another body in a multi-body system. Although the PoE formula is mainly used in robotics, this work aims to demonstrate the utility of the PoE formula as an alternative method for defining and drawing orbits given an orbital elements set. The work also explores the first derivative of the adapted PoE formula in the framework of orbital mechanics, which allows obtaining the state of the satellite (position and velocity) from the orbital elements set using the developed formulation.
