Lagrange top
E662757
The Lagrange top is a classical rigid body in mechanics consisting of a symmetric spinning top with one fixed point in a uniform gravitational field, notable for being one of the standard exactly solvable examples in rotational dynamics.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
integrable system
ⓘ
mechanical system ⓘ rigid body ⓘ |
| describedBy |
Euler angles
NERFINISHED
ⓘ
Euler–Lagrange equations NERFINISHED ⓘ Hamilton’s equations NERFINISHED ⓘ effective potential for nutation angle ⓘ |
| field |
analytical mechanics
ⓘ
classical mechanics ⓘ rigid body dynamics ⓘ |
| hasPart |
center of mass below fixed point
ⓘ
fixed point ⓘ symmetry axis ⓘ |
| hasProperty |
Hamiltonian formulation
ⓘ
Lagrangian formulation ⓘ Poisson bracket structure ⓘ SO(3) symmetry ⓘ admits elliptic function solutions ⓘ admits precession and nutation ⓘ axially symmetric inertia tensor ⓘ conservative system ⓘ conserved component of angular momentum ⓘ conserved energy ⓘ conserved projection of angular momentum on symmetry axis ⓘ conserved projection of angular momentum on vertical axis ⓘ cyclic coordinate for spin angle ⓘ exactly solvable ⓘ integrals of motion exist ⓘ nonlinear equations of motion ⓘ one fixed point ⓘ reduction to one-dimensional effective potential ⓘ rotational symmetry about vertical axis ⓘ separable in Euler angles ⓘ small nutation oscillations ⓘ spinning ⓘ steady precession solutions ⓘ subject to uniform gravitational field ⓘ symmetric ⓘ three degrees of freedom ⓘ |
| namedAfter | Joseph-Louis Lagrange NERFINISHED ⓘ |
| relatedTo |
Euler top
ⓘ
Kovalevskaya top NERFINISHED ⓘ heavy symmetric top ⓘ |
| studiedIn |
advanced mechanics courses
ⓘ
integrable systems theory ⓘ rotational dynamics ⓘ |
| usedAs |
example in textbooks on classical mechanics
ⓘ
standard example of integrable rigid body ⓘ test case for analytical methods in mechanics ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.