Euler top
E662756
The Euler top is a classical rigid body in rotational dynamics that spins freely about a fixed point without external torques, serving as a fundamental example in the study of integrable systems.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
classical mechanical model
ⓘ
integrable system ⓘ mechanical system ⓘ rigid body ⓘ |
| field |
Hamiltonian mechanics
NERFINISHED
ⓘ
classical mechanics ⓘ integrable systems ⓘ rigid body dynamics ⓘ |
| governedBy |
Euler equations for rigid body rotation
ⓘ
Hamiltonian equations of motion ⓘ |
| hasConfigurationSpace | SO(3) NERFINISHED ⓘ |
| hasCoordinateDescription |
body-fixed frame
ⓘ
space-fixed frame ⓘ |
| hasIntegralOfMotion |
components of angular momentum in space frame
ⓘ
squared angular momentum magnitude ⓘ total kinetic energy ⓘ |
| hasMathematicalStructure |
Lie–Poisson system
ⓘ
Poisson manifold ⓘ coadjoint orbit of SO(3) ⓘ |
| hasPhaseSpace | cotangent bundle of SO(3) ⓘ |
| hasProperty |
angular momentum conservation
ⓘ
conservative system ⓘ deterministic dynamics ⓘ energy conservation ⓘ free rotation about a fixed point ⓘ integrals of motion in involution ⓘ no external torques ⓘ three principal moments of inertia ⓘ time-reversible dynamics ⓘ |
| hasSolutionType |
elliptic function solutions
ⓘ
quasi-periodic motion ⓘ |
| hasSpecialCase |
Lagrange top in zero-gravity limit
ⓘ
symmetric top without gravity ⓘ |
| hasSymmetryGroup | rotation group SO(3) NERFINISHED ⓘ |
| hasVariable |
angular momentum vector
ⓘ
angular velocity vector ⓘ principal moments of inertia I1, I2, I3 ⓘ |
| isExampleOf |
Liouville-integrable Hamiltonian system
ⓘ
finite-dimensional integrable model ⓘ torus action in phase space ⓘ |
| namedAfter | Leonhard Euler NERFINISHED ⓘ |
| relatedConcept |
Kovalevskaya top
NERFINISHED
ⓘ
Lagrange top NERFINISHED ⓘ gyroscopic motion ⓘ heavy symmetric top ⓘ |
| usedAs |
canonical example in rigid body dynamics courses
ⓘ
example in Hamiltonian mechanics textbooks ⓘ test case for integrability ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.