An artificial fish moves as a real fish does: by contracting its
muscles. If 
is a muscle, it is contracted by decreasing its
rest length 
. The characteristic undulation of the fish tail
can be achieved by periodically contracting the swimming segment
muscles on one side of the body while relaxing their counterparts on
the other side. We will develop the motor controllers that produce
this muscle coordination in Section 
.
When the fish tail swings, it sets in motion a volume of water. The
inertia of the displaced water produces a reaction force normal to the
fish's body and proportional to the volume of water displaced per unit
time, which propels the fish forward (Fig. ).
Assuming irrotational, incompressible and not very viscid fluid, the instantaneous hydrodynamic force on the surface S of a body due to the fluid is approximately proportional to
where 
is the unit outward normal function over the
surface and 
is the relative velocity function between the
surface and the fluid [Massey1983]. For efficiency, we triangulate
the faces of the fish model between the nodes. For each triangle, we
approximate the hydrodynamic force as
where 
is the viscosity of the fluid medium, A is the area of
the triangle, is its normal, and is its velocity
relative to the water.
The external forces 
(see
Eq. ) at each of the three nodes of the triangle are
incremented by 
.
| Xiaoyuan Tu | January 1996 |
