# Hydrostatic equilibrium¶

We simulate the hydrostatic equilibrium of a box in heave and pitch, comparing the solution given by the linear and nonlinear approximations.

We consider a box with the following dimensions $$(L,B,H) = (8,4,2)m$$, with a center of gravity located at the center of the box. Its mass is taken as

$mass = \dfrac{1}{2} \rho_{water}\times V_{box} = \dfrac{1}{2} \rho_{water}\times L \times B \times H$

An artificial linear damping force is introduced, to make for the hydrodynamic radiation damping. (see Damping force). The diagonal coefficients are taken at $$1E4$$ for the translation and rotation degrees of freedom.

Fig. 24 Decay test in heave, in small amplitude motions : blue = linear approximation, orange = nonlinear approximation

Fig. 25 Decay test in heave, in large amplitude motions : green = linear approximation, red = nonlinear approximation

Fig. 26 Decay test in pitch, in small amplitude motions : violet = linear approximation, brown = nonlinear approximation

Fig. 27 Decay test in pitch, in large amplitude motions : pink = linear approximation, grey = nonlinear approximation