Lagrange top
E662757
The Lagrange top is a classical rigid body in mechanics consisting of a symmetric spinning top with one fixed point in a uniform gravitational field, notable for being one of the standard exactly solvable examples in rotational dynamics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Lagrange top canonical | 2 |
| Poinsot’s central axis | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7419946 — 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: Lagrange top Context triple: [Kovalevskaya top, relatedTo, Lagrange top]
-
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.
On the rotation of a solid body about a fixed point
"On the Rotation of a Solid Body About a Fixed Point" is a landmark mathematical treatise in rigid body dynamics that contributed fundamentally to the theory of differential equations and classical mechanics.
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C.
Taylor–Proudman theorem
The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
-
D.
Lorenz attractor
The Lorenz attractor is a famous chaotic set arising from a simplified model of atmospheric convection, known for its butterfly-shaped trajectory and role as an early example of deterministic chaos in dynamical systems.
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E.
Torqued Ellipses
Torqued Ellipses is a series of monumental, curving steel sculptures by Richard Serra that immerse viewers in disorienting, spiraling spatial experiences.
- 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: Lagrange top Target entity description: The Lagrange top is a classical rigid body in mechanics consisting of a symmetric spinning top with one fixed point in a uniform gravitational field, notable for being one of the standard exactly solvable examples in rotational 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.
On the rotation of a solid body about a fixed point
"On the Rotation of a Solid Body About a Fixed Point" is a landmark mathematical treatise in rigid body dynamics that contributed fundamentally to the theory of differential equations and classical mechanics.
-
C.
Taylor–Proudman theorem
The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
-
D.
Lorenz attractor
The Lorenz attractor is a famous chaotic set arising from a simplified model of atmospheric convection, known for its butterfly-shaped trajectory and role as an early example of deterministic chaos in dynamical systems.
-
E.
Torqued Ellipses
Torqued Ellipses is a series of monumental, curving steel sculptures by Richard Serra that immerse viewers in disorienting, spiraling spatial experiences.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
integrable system
ⓘ
mechanical system ⓘ rigid body ⓘ |
| describedBy |
Euler angles
ⓘ
Euler–Lagrange equations ⓘ
linked to:
Euler–Lagrange equation
Hamilton’s equations ⓘ
linked to:
Hamiltonian mechanics
effective potential for nutation angle ⓘ |
| field |
analytical mechanics
ⓘ
classical mechanics ⓘ rigid body dynamics ⓘ |
| hasPart |
center of mass below fixed point
ⓘ
fixed point ⓘ symmetry axis ⓘ |
| hasProperty |
Hamiltonian formulation
ⓘ
Lagrangian formulation ⓘ Poisson bracket structure ⓘ SO(3) symmetry ⓘ admits elliptic function solutions ⓘ admits precession and nutation ⓘ axially symmetric inertia tensor ⓘ conservative system ⓘ conserved component of angular momentum ⓘ conserved energy ⓘ conserved projection of angular momentum on symmetry axis ⓘ conserved projection of angular momentum on vertical axis ⓘ cyclic coordinate for spin angle ⓘ exactly solvable ⓘ integrals of motion exist ⓘ nonlinear equations of motion ⓘ one fixed point ⓘ reduction to one-dimensional effective potential ⓘ rotational symmetry about vertical axis ⓘ separable in Euler angles ⓘ small nutation oscillations ⓘ spinning ⓘ steady precession solutions ⓘ subject to uniform gravitational field ⓘ symmetric ⓘ three degrees of freedom ⓘ |
| namedAfter | Joseph-Louis Lagrange ⓘ |
| relatedTo |
Euler top
ⓘ
Kovalevskaya top ⓘ heavy symmetric top ⓘ |
| studiedIn |
advanced mechanics courses
ⓘ
integrable systems theory ⓘ rotational dynamics ⓘ |
| usedAs |
example in textbooks on classical mechanics
ⓘ
standard example of integrable rigid body ⓘ test case for analytical methods in mechanics ⓘ |
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: Lagrange top Description of subject: The Lagrange top is a classical rigid body in mechanics consisting of a symmetric spinning top with one fixed point in a uniform gravitational field, notable for being one of the standard exactly solvable examples in rotational dynamics.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lagrange top