This
section contains some more advanced examples that are of interest to
juniors/senior physics majors.
The
problem of paddling a canoe across a river with a downstream current that
varies across the width of the river is considered. The path taken by the
canoe is determined by solving a nonlinear differential equation. In its simplest
form (uniform current) this problem is equivalent to a predatorprey problem.
Placing
a mass (or exerting a force) on a fixed line leads to interesting static and
dynamic behavior. A fixed line is a line that is fixed at both ends.
Interesting
static behavior involves mechanical advantage if the stiffness (i.e. the
value of the equivalent spring constant k) is large enough.
Interesting
dynamic behavior involves crossovers between harmonic and anharmonic behavior when a mass is attached to the line
and dropped.
