4.0 Intro

In hydrostatic terminology, the gravitational and buoyance forces are called restoring forces, and they are equivalent to the spring forces in a mass-damper-spring system.

In the derivation of the restoring forces and moments we will both look at underwater vehicles and surface vessels.

6-DOF equations of motion

$$M\dot{\nu }+C(\nu )\nu +D(\nu )\nu +\underset{1}{\underbrace{g(\eta )}}+\underset{2}{\underbrace{g_0}}=\tau +{\tau }_{wind}+{\tau }_{wave}$$

Term 1 contains the gravitational/ buoyancy terms Term 2 is the ballast control