Coriolis Theorem

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A fundamental theorem describing the relationship between derivatives of the same physical quantity taken in an inertial reference frame and a rotating reference frame. The paper uses it to derive the spacecraft's equations of motion in the lunar body-fixed frame: the velocity in the inertial frame equals the relative velocity in the body-fixed frame plus the cross product of angular velocity and position vector (VI=VL+omega×R). Differentiating this relation and applying Coriolis theorem yields the relative motion equations containing Coriolis and centrifugal accelerations, forming the theoretical basis for the precise soft landing dynamics model with lunar rotation.

Application Value

This technology is a key component of lunar sample return and crewed lunar landing missions.Through precise orbital control and multi-phase maneuver coordination, safe landing or takeoff of spacecraft at predetermined times and locations can be achieved.

Related Concepts

• Jacobi Integral
• Velocity Function
• Non-Gaussian Distribution

References

• 周净扬和周荻 - 2007 - Precise Modeling and Optimal Trajectory Design for Lunar Spacecraft Soft Landing