Small Denominator

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A situation in numerical computation where a denominator approaches zero. In the perturbation equations of unified orbital elements, as inclination i approaches 180°, the denominator of the 1/cos(i/2) factor approaches zero, causing the right-hand side of the equations to spike, forcing the integrator to dramatically reduce step size, and greatly increasing computation. This is the fundamental cause of computational efficiency degradation at i = 180°.

Application Value

The Small Denominator 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.

References

  • 适用于圆锥曲线的统一根数在地月空间目标轨道预报的应用
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Contributors: ouyangjiahong, Ou Yang Jiahong