Reduced Variational Formulations in Free Boundary Continuum Mechanics
We present the material, spatial, and convective representations for elasticity and fluids with a free boundary from the Lagrangian reduction point of view, using the material and spatial symmetries of these systems. The associated constrained variational principles are formulated and the resulting equations of motion are deduced. In addition, we introduce general free boundary continua that contain both elasticity and free boundary hydrodynamics, extend for them various classical notions, and present the constrained variational principles and the equations of motion in the three representations.
Keywords: Symmetry ; Reduction ; Variational principle ; Constraints ; Material representation ; Spatial representation ; Convective representation ; Lagrangian ; Rigid body ; Ideal fluid ; Elastic material
Record created on 2013-02-27, modified on 2016-08-09