Euler–Poisson equations
E662758
The Euler–Poisson equations are a system of differential equations in rigid body dynamics that describe the rotational motion of a rigid body with a fixed point under the influence of external forces such as gravity.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
equations of motion
ⓘ
mathematical model in rigid body dynamics ⓘ system of differential equations ⓘ |
| appliesTo | rigid body with a fixed point ⓘ |
| assumes |
Newtonian mechanics framework
ⓘ
presence of external forces such as gravity ⓘ rigid body with one fixed point ⓘ |
| category |
differential equations of physics
ⓘ
equations of rigid body rotation ⓘ |
| dependsOn |
angular velocity vector of the rigid body
ⓘ
direction cosines of the gravity vector in the body frame ⓘ inertia tensor of the rigid body ⓘ torque due to gravity ⓘ |
| describes |
dynamics of a heavy rigid body in a gravitational field
ⓘ
rotational motion of a rigid body with a fixed point ⓘ |
| dimension | six-dimensional phase space for angular velocity and orientation variables ⓘ |
| expressedIn |
body-fixed coordinate system
ⓘ
principal axes of inertia ⓘ |
| field |
analytical mechanics
ⓘ
classical mechanics ⓘ rigid body dynamics ⓘ |
| governs |
time evolution of angular velocity of a rigid body
ⓘ
time evolution of the direction of the gravity vector in the body frame ⓘ |
| hasProperty |
nonlinearity
ⓘ
time-reversible dynamics in absence of dissipation ⓘ |
| hasSolutionType | integrable in certain classical cases such as Lagrange and Kovalevskaya tops ⓘ |
| hasVariable |
angular momentum vector in body frame
ⓘ
gravity direction vector in body frame ⓘ |
| includes |
Euler equations for angular momentum
NERFINISHED
ⓘ
Poisson equations for orientation ⓘ |
| mathematicalForm | first-order nonlinear ordinary differential equations ⓘ |
| namedAfter |
Leonhard Euler
NERFINISHED
ⓘ
Siméon Denis Poisson NERFINISHED ⓘ |
| relatedTo |
Euler equations (rigid body)
NERFINISHED
ⓘ
Hamiltonian mechanics NERFINISHED ⓘ Lagrangian mechanics NERFINISHED ⓘ Poisson bracket formalism NERFINISHED ⓘ conservation of angular momentum about the fixed point ⓘ conservation of energy in rigid body motion ⓘ |
| usedFor |
analysis of stability of rotational motion
ⓘ
derivation of precession and nutation of rigid bodies ⓘ |
| usedIn |
attitude dynamics of spacecraft with a fixed reference point
ⓘ
celestial mechanics models of rotating bodies ⓘ engineering analysis of gyroscopic devices ⓘ study of Euler top with gravity ⓘ study of Kovalevskaya top ⓘ study of Lagrange top ⓘ study of heavy symmetric top ⓘ |
Referenced by (1)
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