Delaunay variables
E621101
Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Delaunay variables canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6833673 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Delaunay variables Context triple: [Lagrange’s planetary equations, relatedTo, Delaunay variables]
-
A.
Gale transform
The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
-
B.
Lyapunov vector
A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
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C.
Plücker coordinates
Plücker coordinates are a system of homogeneous coordinates used in projective geometry to represent lines (and other subspaces) in higher-dimensional spaces.
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D.
Jacobi integral
The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
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E.
Longuet-Higgins
Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Delaunay variables Target entity description: Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
-
A.
Gale transform
The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
-
B.
Lyapunov vector
A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
-
C.
Plücker coordinates
Plücker coordinates are a system of homogeneous coordinates used in projective geometry to represent lines (and other subspaces) in higher-dimensional spaces.
-
D.
Jacobi integral
The Jacobi integral is a conserved quantity in celestial mechanics and dynamical systems that simplifies the analysis of motion in rotating reference frames, particularly in the restricted three-body problem.
-
E.
Longuet-Higgins
Longuet-Higgins is the surname of a notable British family that includes influential figures in theoretical chemistry, cognitive science, and mathematics.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
action–angle variables
ⓘ
canonical variables ⓘ set of orbital elements ⓘ |
| appliesTo |
restricted three-body problem
ⓘ
two-body problem ⓘ |
| assumes | central gravitational potential ⓘ |
| basedOn | Keplerian orbital elements NERFINISHED ⓘ |
| correspondsToOrbitalElement |
argument of periapsis
ⓘ
longitude of ascending node ⓘ mean anomaly ⓘ |
| correspondsToOrbitalElement |
eccentricity
ⓘ
inclination ⓘ semi-major axis ⓘ |
| definedIn | phase space of orbital elements ⓘ |
| enables |
averaging over fast angles
ⓘ
separation of fast and slow orbital variables ⓘ |
| field |
astrodynamics
ⓘ
dynamical astronomy ⓘ |
| hasActionVariable |
D
ⓘ
G ⓘ H ⓘ |
| hasAngleVariable |
g
ⓘ
h ⓘ ℓ ⓘ |
| hasComponent |
D
ⓘ
G ⓘ H ⓘ g ⓘ h ⓘ ℓ ⓘ |
| introducedBy | Charles-Eugène Delaunay NERFINISHED ⓘ |
| isCanonicalWithRespectTo | standard symplectic form ⓘ |
| isGeneralizationOf | Keplerian elements in Hamiltonian form ⓘ |
| relatedTo |
Poincaré variables
NERFINISHED
ⓘ
canonical transformations in mechanics ⓘ |
| usedFor |
analysis of orbital motion
ⓘ
analytical theory of planetary motion ⓘ lunar theory ⓘ perturbation theory in celestial mechanics ⓘ satellite orbit perturbation analysis ⓘ simplification of Hamiltonian formulation of orbital dynamics ⓘ |
| usedIn |
Hamiltonian perturbation theory
ⓘ
Lagrange planetary equations NERFINISHED ⓘ celestial mechanics ⓘ study of long-term orbital evolution ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Delaunay variables Description of subject: Delaunay variables are a set of canonical action-angle variables used in celestial mechanics to simplify the analysis of orbital motion and perturbations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.