Index
accessory equations, 174
accessory variational problem, 151
Atwood’s machine, 109, 137
autonomous, 65, 86
Bernoulli equation, 147
Bernoulli–Euler beam theory, 72
brachistochrone, 1–4, 18, 59–61, 64,
196, 203, 267, 273, 274
on a cylinder, 66
terrestrial, 5–7, 19, 66
to a vertical line, 212
with variable endpoints, 211
c-discriminant, 157, 207, 258
canonical equations, 90–92, 105,
190, 270
canonical momenta, 88–92, 269,
270
cantilever beam, 71–76, 103, 123
Carath´ eodory equations, 269
catenary, 53–56, 58, 65, 108,
160–167
catenoid, 15–17, 23, 63, 160–167
characteristic, 219–222, 224, 226,
238, 240, 244
chute-the-chute, 212
circle of latitude, 62, 63
complementary curve of descent, 20
condition(s)
Euler–Lagrange, 41, 245
Jacobi, 147, 154, 155, 160, 165,
167–170, 172, 190, 232, 245,
252, 258
Legendre, 142–144, 158, 160, 169,
172, 184, 245, 251, 252, 254
natural boundary, 191, 194–197,
200, 211
necessary, 31, 172, 245
second-variation, 141
strengthened Jacobi, 173, 235,
237, 240, 259, 260, 263, 264
strengthened Legendre, 143, 158,
173, 235, 236, 240, 266
sufficient, 173–175, 255, 263, 264,
266, 273
transversality, 197, 200–207, 212,
213, 215, 217, 227, 242
variable-endpoint, 176
weak sufficiency, 149
Weierstrass, 242–247, 254, 273
Weierstrass–Erdmann corner,
176, 215–219, 221, 222
conjugate point, 155, 159, 165, 168,
237, 240, 258, 266
conjugate value, 155, 159
constraint(s)
holonomic, 109, 110, 129–132
inequality, 112, 136
295
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