Orbitallattice

Orbitallattice is a theoretical framework that combines lattice theory with orbital dynamics to model the structure of possible orbital configurations under perturbations. In this approach, individual orbital states—described by standard orbital elements or action-angle coordinates—are treated as elements of a partially ordered set, where the order reflects refinement under allowed perturbations. When the set forms a lattice, any two states have a least upper bound and a greatest lower bound, interpreted as combined resonant states and common refinements, respectively.

Construction and notation: The elements may be taken as equivalence classes of orbital elements under a chosen symmetry group. The grading can be defined by an energy-like quantity or a stability measure. Covering relations encode elementary transitions such as resonance capture, secular drift, or perturbation by oblateness. The join and meet operations correspond to the least common refinement and the most specific common refinement of two orbital states, respectively.

Relation to existing concepts: Orbitallattices draw on lattice theory and dynamical systems, offering a combinatorial perspective on phase-space structure. They are distinct from physical lattices in space and from standard numerical trajectory methods; instead, they provide a discrete, hierarchical view of orbital configurations and their transitions.

Applications: Potential uses include visualization of resonance networks, organization of feasible transfer orbits, and structured stability analysis. They can complement numerical simulations by providing a compact, symbolic representation of possible state evolutions under perturbations.

Status: Orbitallattice remains largely theoretical and exploratory, with ongoing work to establish formal properties, computational methods, and practical relevance for mission design or celestial mechanics.