Jacobi last multiplier
E182752
The Jacobi last multiplier is a mathematical tool introduced by Carl Gustav Jacob Jacobi for integrating systems of differential equations by providing an integrating factor that simplifies them to solvable form.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Jacobi last multiplier canonical | 2 |
| Jacobi multiplier | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1615220 — 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 last multiplier Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi last multiplier]
-
A.
Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
-
B.
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.
-
C.
Lie bracket
The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
-
D.
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.
-
E.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
- 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 last multiplier Target entity description: The Jacobi last multiplier is a mathematical tool introduced by Carl Gustav Jacob Jacobi for integrating systems of differential equations by providing an integrating factor that simplifies them to solvable form.
-
A.
Carathéodory–Jacobi–Lie theorem
The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
-
B.
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.
-
C.
Lie bracket
The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
-
D.
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.
-
E.
Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
- F. None of above. chosen
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
method for differential equations ⓘ |
| appliesTo |
nonlinear differential equations
ⓘ
ordinary differential equations ⓘ systems of first-order differential equations ⓘ |
| characterizedAs | multiplicative integrating factor ⓘ |
| field |
classical mechanics
ⓘ
differential equations ⓘ dynamical systems ⓘ mathematical analysis ⓘ |
| goal |
construction of solvable forms of equations
ⓘ
simplification of differential systems ⓘ |
| hasAlternativeName |
Jacobi last multiplier
ⓘ
surface form:
Jacobi multiplier
|
| hasProperty |
can be used to generate Lagrangians for given equations of motion
ⓘ
coordinate dependent ⓘ |
| historicalPeriod | 19th century mathematics ⓘ |
| introducedBy | Carl Gustav Jacob Jacobi ⓘ |
| namedAfter | Carl Gustav Jacob Jacobi ⓘ |
| relatedTo |
Hamiltonian mechanics
ⓘ
Jacobi determinant ⓘ Jacobian matrix ⓘ Lagrangian function ⓘ Lie symmetries ⓘ first integral ⓘ integrating factor ⓘ inverse problem of the calculus of variations ⓘ |
| use |
construction of integrating factors
ⓘ
derivation of first integrals ⓘ integration of systems of differential equations ⓘ reduction of differential equations to solvable form ⓘ study of Lagrangian structures ⓘ |
| usedIn |
classical dynamics
ⓘ
geometric theory of differential equations ⓘ theory of symmetries of differential equations ⓘ |
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 last multiplier Description of subject: The Jacobi last multiplier is a mathematical tool introduced by Carl Gustav Jacob Jacobi for integrating systems of differential equations by providing an integrating factor that simplifies them to solvable form.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Jacobi multiplier
subject surface form:
Carl Gustav Jacob Jacobi