Variational Equation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The linearized Hamiltonian system along a reference extremal, governing the propagation of state-costate perturbations. Its solutions are Jacobi fields, used to compute conjugate points and verify second-order optimality conditions. The coefficient matrix is the Jacobian of the Hamiltonian vector field evaluated along the reference trajectory.

Application Value

This term has application value in the design and analysis of cislunar space missions, supporting trajectory design, mission planning, and system optimization. Researchers can analyze its physical mechanisms and engineering applicability based on specific mission requirements to advance cislunar space exploration technology.

  • Delta-v
  • Sigmoid Function
  • Deep Residual Network, ResNet
  • Instantaneous Classical Orbit Elements

References

  • Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem
  • Gómez et al. 2001, Ch.1,3
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Contributors: ouyangjiahong, Ou Yang Jiahong