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.
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 NERFINISHED ⓘ |
| developedBy | Joseph-Louis Lagrange NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| relatedTo |
Gauss’s form of the planetary equations
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
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