Lambert’s problem is the two-point boundary value problem for Keplerian dynamics. The parameter and solution space is surveyed for both the zero- and multiple-revolution problems, including a detailed look at the stress cases that typically plague Lambert solvers. The problem domain, independent of formulation, is shown to be rectangular for each revolution case, making the elusive initial guess and the solution itself amenable for interpolation. Biquintic splines are implemented to achieve continuous derivatives and quick evaluation. Resulting functions may be used directly as low-fidelity solutions or used with a single update iteration without safeguards. A concise, improved vercosine formulation of the Lambert problem is presented, including new singularity-free and precision-saving equations. The interpolation scheme is applied for up to 100 revolutions. The domain considered includes all practically conceivable flight times, and every possible geometry except a small region near the only physical singularity of the problem: the equal terminal vector case. The solutions are archived and benchmarked for accuracy, memory footprint, and speed. For typical scenarios, users can expect $$\sim 6$$ or more digits of velocity vector accuracy using an interpolated solution without iteration. Using a single, unguarded iteration leads to solutions with near machine precision accuracy over the full domain, including the most extreme scenarios. Depending on desired resolution, coefficient files vary in size from $$\sim 3$$ to 65 MB for each revolution case. Evaluation runtimes vary from $$\sim 2$$ to 5 times faster than the industry benchmark Gooding algorithm. The coefficient files and driver routines are provided online. While the method is currently demonstrated on the vercosine formulation, the 2D interpolation scheme stands to benefit all Lambert problem formulations.

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关于每个兰伯特问题的解

兰伯特问题是开普勒动力学的两点边值问题。针对零旋转和多旋转问题对参数和解空间进行了调查，包括详细查看通常困扰 Lambert 求解器的应力情况。与公式无关的问题域对于每个旋转案例显示为矩形，使得难以捉摸的初始猜测和解决方案本身适合插值。实施双五次样条以实现连续导数和快速评估。结果函数可以直接用作低保真解决方案，也可以在没有保护措施的情况下与单个更新迭代一起使用。提出了兰伯特问题的简洁、改进的 vercosine 公式，包括新的无奇点和精度节省方程。插值方案适用于最多 100 转。所考虑的域包括所有实际上可以想象的飞行时间，以及除了问题唯一物理奇点附近的一个小区域之外的所有可能的几何形状：相等的终端向量情况。这些解决方案在准确性、内存占用和速度方面进行了存档和基准测试。对于典型场景，用户可以使用无需迭代的插值解决方案来期望 $$\sim 6$$ 或更多位数的速度矢量精度。使用单一的、不受保护的迭代会导致解决方案在整个域上具有接近机器精度的精度，包括最极端的场景。根据所需的分辨率，对于每个旋转情况，系数文件的大小从 $$\sim 3$$ 到 65 MB 不等。评估运行时间从 $$\sim 2$$ 到比行业基准 Gooding 算法快 5 倍不等。系数文件和驱动程序在线提供。虽然该方法目前在 vercosine 公式上进行了演示，但 2D 插值方案有利于所有 Lambert 问题公式。