Kirchhoff equations [SEP] named after
Kirchhoff equations
In fluid dynamics, the Kirchhoff equations, named after Gustav Kirchhoff, describe the motion of a rigid body in an ideal fluid.
where formula_2 and formula_3 are the angular and linear velocity vectors at the point formula_4, respectively; formula_5 is the moment of inertia tensor, formula_6 is the body's mass; formula_7 is
a unit normal to the surface of the body at the point formula_4;
formula_9 is a pressure at this point; formula_10 and formula_11 are the hydrodynamic
torque and force acting on
load formula_41 per unit area is
where
Dynamics of thin Kirchhoff plates.
The dynamic theory of plates determines the propagation of waves in the plates, and the study of standing waves and vibration modes.
Dynamics of thin Kirchhoff plates Governing equations.
The governing equations for the dynamics of a Kirchhoff–Love plate are
where, for a plate with density formula_44,
and
The figures below show some vibrational modes of a circular plate.
Dynamics of thin Kirchhoff plates Isotropic plates.
The governing equations simplify