Canonical Transformation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A transformation of phase space variables that preserves the canonical form of Hamilton's equations. The new variables still satisfy Hamilton's canonical equations, and the Jacobian determinant equals 1, meaning the transformation preserves phase space volume (Liouville's theorem). Canonical transformation is a core technique in celestial mechanics for simplifying perturbation problems by choosing appropriate variables to separate fast and slow motions.

Application Value

在轨道力学分析中，This摄动因素is轨道预报误差的main来源之一。准确建模This效应有助于提高轨道预测精度，支持轨道维持和碰撞预警等应用。

Related Concepts

• 约束转化非线性规划（Constraint Conversion to Nonlinear Programming）
• 全局搜索（Global Search）
• 万有引力常数（Universal Gravitational Constant）
• 再入航迹角（Reentry Flight Path Angle）

References

• Ding et al., 2025 — Cislunar Space Situational Awareness via Earth-Moon Resonant Orbits
• Meyer和Offin - 2017