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.
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
conserved quantity
ⓘ
first integral ⓘ integral of motion ⓘ |
| appliesTo | Kovalevskaya top NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| relatedTo |
Euler–Poisson equations
NERFINISHED
ⓘ
Kovalevskaya case of a heavy rigid body about a fixed point NERFINISHED ⓘ |
| requiresCondition | specific ratio of principal moments of inertia of the rigid body ⓘ |
| roleInSystem |
additional conserved quantity
ⓘ
ensures complete integrability ⓘ |
| studiedIn |
Hamiltonian mechanics
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.