Sub-Riemannian Structure

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A geometric structure defined on a manifold by a distribution of rank less than the manifold dimension together with a Riemannian metric. The control vector field distribution of the circular restricted three-body problem combined with the thrust direction field in the rotating frame constitutes a sub-Riemannian structure.

Application Value

This concept plays an important role in trajectory optimization and mission planning applications.

Related Concepts

• Jacobi Integral
• Coriolis Theorem
• Velocity Function

References

• Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)