Hyperelliptic Curve

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The algebraic curve appearing in the averaged Hamiltonian integral. For circular target orbits (p_θ=0), the integral reduces to a genus-2 hyperelliptic curve, affecting both the structure of the optimal control and numerical difficulty.

Application Value

The Hyperelliptic Curve plays a significant role in cislunar space mission design, analysis, and control. In orbital design, it can be leveraged for transfer trajectory optimization; in navigation and control, it improves mission execution precision and reliability; in system analysis, it facilitates deeper understanding of complex multi-body dynamical behavior, guiding mission planning and risk assessment.

  • J2-Invariant Orbit
  • Interior Point Optimization
  • N-Body Dynamics
  • Start-End State Constraint

References

  • Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)
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Contributors: ouyangjiahong, Ou Yang Jiahong