Higher-order methods such as state transition tensors (STTs) have shown promise for a variety of applications in astrodynamics, but can be limited in their use due to their potentially large computational and storage requirements. In this paper we present a method for approximating STTs by aligning the STTs with particularly unstable directions. This strategy allows us to isolate the most important terms in the higher-order STTs and ignore any less important terms. This method, which we call directional state transition tensors (DSTTs), is applied to several examples in two- and three-body dynamic systems, and it is shown to perform well for both nonlinear state and state uncertainty propagation. The method produces similar results to the full STTs, but requires significantly fewer elements to be stored, which can result in up to $1000\times$ improvements in speed for nonlinear uncertainty propagation computations. DSTTs are promising for expanding the use of STTs to situations with highly nonlinear dynamics but limited computational resources, such as on-board a spacecraft.

状态转移张量 (STT) 等高阶方法已显示出在天体动力学中的各种应用前景，但由于其潜在的大量计算和存储需求，它们的使用可能会受到限制。在本文中，我们提出了一种通过将 STT 与特别不稳定的方向对齐来近似 STT 的方法。这种策略使我们能够隔离高阶 STT 中最重要的术语，并忽略任何次要的术语。我们将这种方法称为定向状态转移张量 (DSTT)，应用于二体和三体动态系统中的多个示例，结果表明它在非线性状态和状态不确定性传播方面表现良好。该方法产生与完整 STT 相似的结果，但需要存储的元素要少得多，这可能导致多达$1000\times$非线性不确定性传播计算速度的改进。DSTT 有望将 STT 的使用扩展到具有高度非线性动力学但计算资源有限的情况，例如在航天器上。