Jacobi integral
E182755
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Jacobi integral canonical | 3 |
| Jacobi constant | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1615224 — 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: Jacobi integral Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi integral]
-
A.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
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B.
Lagrange’s planetary equations
Lagrange’s planetary equations are a set of differential equations in celestial mechanics that describe how the orbital elements of a body evolve over time under perturbing forces.
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C.
Gauss’s planetary equations
Gauss’s planetary equations are a set of differential equations in celestial mechanics that describe how a planet’s orbital elements change over time under the influence of perturbing forces.
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D.
Kovalevskaya top
The Kovalevskaya top is a famous integrable case of the motion of a rigid body about a fixed point in classical mechanics, discovered and analyzed by mathematician Sofia Kovalevskaya.
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E.
Laplace resonance
Laplace resonance is a three-body orbital resonance in which the orbital periods of Jupiter’s moons Io, Europa, and Ganymede are linked in a precise 1:2:4 ratio, strongly affecting their dynamics and internal heating.
- 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: Jacobi integral Target entity description: 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.
-
A.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
-
B.
Lagrange’s planetary equations
Lagrange’s planetary equations are a set of differential equations in celestial mechanics that describe how the orbital elements of a body evolve over time under perturbing forces.
-
C.
Gauss’s planetary equations
Gauss’s planetary equations are a set of differential equations in celestial mechanics that describe how a planet’s orbital elements change over time under the influence of perturbing forces.
-
D.
Kovalevskaya top
The Kovalevskaya top is a famous integrable case of the motion of a rigid body about a fixed point in classical mechanics, discovered and analyzed by mathematician Sofia Kovalevskaya.
-
E.
Laplace resonance
Laplace resonance is a three-body orbital resonance in which the orbital periods of Jupiter’s moons Io, Europa, and Ganymede are linked in a precise 1:2:4 ratio, strongly affecting their dynamics and internal heating.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
conserved quantity
ⓘ
first integral ⓘ integral of motion ⓘ scalar quantity ⓘ |
| alsoKnownAs |
Jacobi constant
ⓘ
linked to:
Jacobi integral
|
| appliesTo |
circular restricted three-body problem
ⓘ
motion in rotating reference frames ⓘ restricted three-body problem ⓘ |
| assumes |
Newtonian gravity
ⓘ
linked to:
law of universal gravitation
circular orbits of the primaries in the circular restricted three-body problem ⓘ point-mass primaries ⓘ |
| category |
conservation laws in classical mechanics
ⓘ
invariants in dynamical systems ⓘ |
| dependsOn |
angular velocity of the rotating frame
ⓘ
gravitational parameters of the primaries ⓘ positions of the small body in rotating coordinates ⓘ velocities of the small body in rotating coordinates ⓘ |
| field |
celestial mechanics
ⓘ
dynamical systems ⓘ |
| historicalPeriod | 19th century ⓘ |
| influences |
classification of periodic orbits
ⓘ
existence of transit and non-transit orbits ⓘ |
| mathematicalForm | sum of kinetic energy term and effective potential term in rotating frame ⓘ |
| namedAfter | Carl Gustav Jacob Jacobi ⓘ |
| notConservedIn | non-rotating inertial frame ⓘ |
| property |
constant along trajectories of the restricted three-body problem
ⓘ
invariant under time evolution in the rotating frame ⓘ |
| relatedTo |
Coriolis force
ⓘ
linked to:
Coriolis effect
Hill regions ⓘ Lagrange points ⓘ centrifugal potential ⓘ effective potential in rotating frame ⓘ energy integral ⓘ zero-velocity curves ⓘ |
| role |
defines zero-velocity surfaces
ⓘ
provides energy-like invariant in rotating frame ⓘ simplifies analysis of motion in rotating frames ⓘ |
| usedFor |
analyzing motion near Lagrange points
ⓘ
characterizing allowed regions of motion ⓘ mission design in astrodynamics ⓘ studying stability of orbits ⓘ |
| usedIn |
astrodynamics
ⓘ
space mission trajectory design ⓘ study of asteroid and comet motion in planetary systems ⓘ study of natural satellite dynamics ⓘ |
| validIn | synodic (rotating) coordinate system ⓘ |
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: Jacobi integral Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.