论文标题
兰伯特（Lambert
A Lambert's Problem Solution via the Koopman Operator with Orthogonal Polynomials
论文作者
论文摘要
兰伯特的问题长期以来在太空运营的背景下进行了研究。它的解决方案实现了准确的轨道测定和航天器指导。这项工作为Lambert使用Koopman操作员（KO）提供了分析解决方案。与文献中以前的方法相反，KO通过寻求将非线性动力学嵌入到全局线性表示中的转换来提供非线性系统的分析。我们解决Lambert Solutions的新方法考虑了系统在相位平面上的特征值的位置，评估了精确的状态过渡多项式图，以进行动力学的计算有效传播。将所使用的方法和发现的多革命解决方案的准确性和性能与文献中的其他技术进行了比较，从而强调了与经典数值方法相比，新开发的分析方法的好处。
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator (KO). In contrast to previous methods in the literature, the KO provides the analysis of a nonlinear system by seeking a transformation that embeds the nonlinear dynamics into a global linear representation. Our new methodology to solve for Lambert solutions considers the position of the system's eigenvalues on the phase plane, evaluating accurate state transition polynomial maps for a computationally efficient propagation of the dynamics. The methodology used and multiple-revolution solutions found are compared in accuracy and performance with other techniques found in the literature, highlighting the benefits of the newly developed analytical approach over classical numerical methodologies.
