Lagrange’s variation of parameters method
E621100
analytical method
mathematical technique
method in celestial mechanics
method in differential equations
perturbation method
Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lagrange’s variation of parameters method canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6833659 — 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’s variation of parameters method Context triple: [Lagrange’s planetary equations, basedOn, Lagrange’s variation of parameters method]
-
A.
Linear Differential Equations and Their Applications
"Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
-
B.
Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
"Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
-
C.
Cauchy–Euler equation
The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
-
D.
Laplace method
The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
-
E.
d’Alembert’s formula
d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
- 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’s variation of parameters method Target entity description: Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
-
A.
Linear Differential Equations and Their Applications
"Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
-
B.
Bogoliubov–Mitropolsky asymptotic methods in nonlinear oscillations
"Bogoliubov–Mitropolsky Asymptotic Methods in Nonlinear Oscillations" is a classic mathematical monograph that develops systematic asymptotic techniques for analyzing and approximating solutions of nonlinear oscillatory systems.
-
C.
Cauchy–Euler equation
The Cauchy–Euler equation is a type of linear ordinary differential equation with variable coefficients that often appears in problems with power-law or scale-invariant behavior.
-
D.
Laplace method
The Laplace method is an asymptotic technique in mathematical analysis used to approximate integrals, especially those dominated by contributions near a maximum point of the integrand.
-
E.
d’Alembert’s formula
d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
analytical method
ⓘ
mathematical technique ⓘ method in celestial mechanics ⓘ method in differential equations ⓘ perturbation method ⓘ |
| appliesTo |
orbital element equations
ⓘ
ordinary differential equations ⓘ |
| assumes | small perturbing accelerations ⓘ |
| basedOn |
osculating element concept
ⓘ
two-body Keplerian motion ⓘ |
| canHandle |
atmospheric drag effects
ⓘ
gravitational perturbations ⓘ non-gravitational perturbations ⓘ oblateness perturbations ⓘ radiation pressure perturbations ⓘ third-body perturbations ⓘ |
| category | theory of orbital perturbations ⓘ |
| contrastsWith | numerical integration of equations of motion ⓘ |
| derives |
Lagrange planetary equations
ⓘ
linked to:
Lagrange’s planetary equations
|
| developedBy | Joseph-Louis Lagrange ⓘ |
| field |
applied mathematics
ⓘ
astrodynamics ⓘ celestial mechanics ⓘ differential equations ⓘ orbital mechanics ⓘ |
| goal |
account for perturbations to ideal motion
ⓘ
determine time evolution of orbital elements ⓘ |
| historicalPeriod | 18th century ⓘ |
| influenced | modern orbit determination techniques ⓘ |
| involves |
time-dependent orbital elements
ⓘ
transformation between state vectors and elements ⓘ |
| mathematicalNature | analytical perturbation expansion ⓘ |
| namedAfter | Joseph-Louis Lagrange ⓘ |
| relatedTo |
Gauss’s form of the planetary equations
ⓘ
linked to:
Gauss’s planetary equations
classical perturbation theory ⓘ variation of constants method ⓘ |
| requires |
expression for perturbing acceleration
ⓘ
unperturbed fundamental solution ⓘ |
| typicalOutput |
differential equations for orbital elements
ⓘ
time-varying Keplerian elements ⓘ |
| usedIn |
long-term orbital evolution studies
ⓘ
planetary motion analysis ⓘ satellite orbit prediction ⓘ space mission design ⓘ |
| uses |
Keplerian reference orbit
ⓘ
osculating orbital elements ⓘ perturbing forces ⓘ |
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’s variation of parameters method Description of subject: Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.