6 The Physics of Motion
Forward dynamics is used to approximate the key physical affects required
for a swimmer to do its thing, most importantly - the interplay between
momentum generated by sweeping body parts, and drag, and the effects of
torque in generating angular acceleration.
Swimmer's bodies are approximated as 2D rigid bodies composed of
line segments, which can change internally via the autonomous bending
of joints. A swimmer's internal geometry cannot be changed by outside
forces. In a 3D version of this world, these line segments would roughly
correspond to thin cylinders of equal size, shape, and mass. A swimmer's
mass equals the sum of all limb segment lengths times a mass constant.
As stated before, fluid flow is not calculated in this model -
the fluid is assumed to be fixed in a world frame. Its job is simply
to supply friction to give the swimmers something to work against.
Proportional to a friction constant, the motion of each limb segment
creates a force proportional to the sine of the angle between the
segment orientation and the segment velocity.
Angular momentum is affected by torques created by each limb
segment's force, in relation to the center of mass. In each time step,
the accumulation of all linear and angular forces generated by individual
segment motions are summed up to create net linear and angular accelerations.
This physics model is not comprehensive, but sufficient for the purposes
of this study. And it allows for both paddling-type motions and undulating-type
motions to be affective in propelling the body, assuming there is minimal drag
caused by other body parts. It also supplies a variable corresponding to the
magnitude of total forces exerted on the water, which is used to approximate
the expenditure of energy in a swimmer.
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