revenue, 204
river crossing, 188–189, 199–202
saddle point, see equilibrium point
scaling, 127–130, 163–164, 188
second variation, see variation
semi-field, 107, 113
separatrix, 212
simple broken extremal, see
extremal
simply connected, 91
singular control, see control
smooth, 8
state, 128, 135
restricted, 196–197
Stokes’ theorem, 94
strengthened Legendre condition,
see Legendre condition
strong minimum, 67, 73, 110, 116
strong variation, see variation, 81
sufficient condition
fundamental, 102, 219
surface of revolution
minimum area of, 6, 14–15, 17,
25, 32, 126
switching
curve, 152, 157, 178
function, 150, 160
synthesis of optimal control, see
control
target, 137
general, 167–176
Taylor series, 52, 53
Taylor’s theorem, 137, 171
with remainder, 78, 103
terminal cost, see cost
terminality condition, 136, 141
time-optimal control, see control
total variation, see variation
trajectory
optimal, 136–142, 144, 209
nonunique, 202
transversality conditions, 86–87,
174–176, 179–180
trial curve, 4, 9, 41, 51, 73
two-parameter, 121
trial function, 4, 46, 74, 81
tumor growth, 163
variation
admissible, 10–12
first, 53
second, 53
strong, 67, 73–74, 81
total, 52, 53, 102
weak, 9, 67, 73–74, 81
velocity, 2
weak minimum, 67, 73
weak variation, see variation
Weierstrass’s excess function, see
excess function
Weierstrass’s necessary condition,
see necessary condition
Weierstrass-Erdmann conditions,
see corner
wildlife management, 203, 218
Zermelo’s problem, 183–189,
197–202
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