Kovalevskaya integral
E662759
The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kovalevskaya integral canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7419954 — 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: Kovalevskaya integral Context triple: [Kovalevskaya top, hasIntegralOfMotion, Kovalevskaya integral]
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A.
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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B.
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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C.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
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D.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
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E.
Cauchy–Kovalevskaya theorem
The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
- 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: Kovalevskaya integral Target entity description: The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
-
A.
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.
-
B.
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.
-
C.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
-
D.
Kolmogorov–Arnold–Moser theory
Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
-
E.
Cauchy–Kovalevskaya theorem
The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
conserved quantity
ⓘ
first integral ⓘ integral of motion ⓘ |
| appliesTo | Kovalevskaya top ⓘ |
| associatedWith | Kovalevskaya exponents and special inertia relations ⓘ |
| category | conservation laws in mechanics ⓘ |
| contributesTo | complete set of independent integrals for the Kovalevskaya top ⓘ |
| dependsOn |
angular velocities of the rigid body
ⓘ
direction cosines of the gravity vector ⓘ |
| ensures | Liouville integrability of the Kovalevskaya top ⓘ |
| field |
classical mechanics
ⓘ
integrable systems ⓘ rigid body dynamics ⓘ |
| historicalContext | discovered in the 19th century ⓘ |
| independence | functionally independent of energy and momentum integrals ⓘ |
| mathematicalForm | quartic polynomial in phase-space variables (up to canonical transformations) ⓘ |
| namedAfter |
Sofya Kovalevskaya
ⓘ
linked to:
Sofia Kovalevskaya
|
| relatedTo |
Euler–Poisson equations
ⓘ
Kovalevskaya case of a heavy rigid body about a fixed point ⓘ
linked to:
Kovalevskaya top
|
| requiresCondition | specific ratio of principal moments of inertia of the rigid body ⓘ |
| roleInSystem |
additional conserved quantity
ⓘ
ensures complete integrability ⓘ |
| studiedIn |
Hamiltonian mechanics
ⓘ
theory of integrable Hamiltonian systems ⓘ |
| timeDerivative | zero along solutions of the Kovalevskaya top equations ⓘ |
| togetherWith |
area integral
ⓘ
energy integral ⓘ geometric integral ⓘ |
| typeOfConservation | nontrivial polynomial integral ⓘ |
| usedIn |
analysis of exact solutions for the Kovalevskaya top
ⓘ
separation of variables for the Kovalevskaya top ⓘ |
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: Kovalevskaya integral Description of subject: The Kovalevskaya integral is an additional conserved quantity that makes the motion of the Kovalevskaya top exactly integrable in classical rigid body dynamics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.