Jacobian Matrix

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A matrix composed of partial derivatives of multivariable functions, describing the local linear mapping from one vector space to another. In debris cloud probability density calculation, the Jacobian matrix JF = dr2/dv1 describes the mapping from initial velocity space to terminal position space. Its absolute determinant |det JF| appears in the probability density transformation formula, reflecting how spatial mapping amplifies or reduces density.

Application Value

偏导数阵是地月空间研究的基础理论和方法。在实际应用中，该概念为轨道设计、导航计算和动力学分析提供了理论支撑，是理解更复杂空间任务问题的前提。

Related Concepts

• 牛顿万有引力定律（Newton's Law of Gravitation）
• 三角级数（Trigonometric Series）
• 发射三要素（Three Launch Elements）
• 伪势（Pseudo-Potential）

References

• Debris Cloud Evolution in Cislunar Space Using Eulerian Perspective Method
• Kikuchi et al. - 2024 - Comparison of transfer trajectory to NRHO and operation plan for logistics resupply mission to gateway
• Spreen 2021