Index 711
Hamilton equations, 428
Hamilton portrait, 416, 426, 428, 429, 431, 543, 546,
548
Hammer projection, 601
– ellipsoidal, 601, 616
– equiareal modified azimuthal, 33, 36
– retroazimuthal, 10
– – ID card, 10
Hasse diagram, 501–503
Hausdorff axiom of separation, 113
Hausdorff topological space, 113
Helmholtz differential equation, 61, 64
Hesse form, 37
Hesse matrix, 1, 81, 643
Hilbert invariants, 83
Hodge star operator, 102–104, 528
homeomorphism, 113, 114
Hooke matrices, 84
horizontal coordinate mean, 576
Hotine Oblique Mercator Projection (HOM), 113,
359
inclination, 132
indirect problem, 142
initial value problem, 426, 427, 429
initial values, 415
integrability conditions, 52
international reference ellipsoid, 113
inverse transformation, 151
Io, 637, 655
isometric, 48
isometric coordinates, see coordinates, conformal,
313, 316
isometric latitude, 264
isometry, 80
isoparametric mapping, 61
isothermal, 48
isothermal coordinates, see coordinates, conformal,
316
Jacobi matrix, 1, 5
Kartenwechsel, 11, 113, 454
Killing equations, 125
Killing symmetry, 126
Killing vectors, 113, 122–126, 129, 143
Korn–Lichtenstein equations, 43, 46, 48–51, 53,
55–57, 62, 64, 65, 97, 101, 313, 527
Krassowsky reference ellipsoid, 469
Kronecker delta, 361
Kronecker–Zehfuss product, 363
Lagrange function, 2
Lagrange multiplier, 2
Lagrange portrait, 416, 426, 428, 543, 546, 547
Lagrange projection, 161, 193
Lambert azimuthal, 391
Lambert conformal conic mapping, 405
Lambert conformal mapping, 409
Lambert cylindrical equal area projection, 276, 278
Lambert map, 161, 388
Lambert mapping, 379, 382, 386–388, 391, 405, 406,
409, 414
Lambert projection, 569
Laplace equation of harmonicity, 48
Laplace–Beltrami equations, 51–53, 55, 56, 62, 313,
325, 359–362, 529, 530
Laplace–Beltrami operator, 49, 50, 56, 64
least squares, 453, 460
left metric tensor, 7
Legendre recurrence, 416, 426–428, 434
Legendre series, see Legendre recurrence
length distortion, 11, see stretch
lexicographic order, 503
L’Hˆ opital Rule, 617
Lie recurrence, 416, 426, 429, 430, 433, 565
Lie series, see Lie recurrence
local datum, 469, 490
local reference system, 453
loxodrome, 273
mapping
– biaxial ellipsoid-of-revolution to sphere, 32
– concircular, 1
– conformal, 1, 32, 42, 43, 46, 48, 70, 72, 80, 83, 85,
86, 97, 101, 102, 105, 106, 221, 325, 359–361, 369,
406–409, 411–414, 497, 505, 519, 527
– conic, 405–407, 410, 414
– double projection, 32
– ellipsoid-of-revolution to cone, 405
– ellipsoid-of-revolution to cylinder, 313, 359
– ellipsoid-of-revolution to sphere, 2, 5, 39, 41, 53,
55, 62, 76, 83
– ellipsoid-of-revolution to tangential plane, 221
– equiareal, 1, 19, 20, 74, 76, 78, 79, 83, 85, 86, 111,
221, 406
– equidistant, 1, 42, 53, 55, 56, 75, 82, 83, 111, 221,
406, 411, 412, 414
– geodesic, 1
– geodetic, 415–417, 433, 439
– harmonic, 1
– isoparametric, 2–5, 7, 32, 39, 61, 70
– Jacobi, 4, 6
– loxodromic, 1
– mixed cylindric, 569, 589, 601, 637
– northern hemisphere to equatorial plane, 19, 33
– oblique orthogonal, 92, 93
– orthogonal, 19, 23, 28, 33–35, 92, 122, 638
– perspective, 221, 240
– pseudo-azimuthal, 10
– pseudo-cylindrical, 19, 589
– relation preserving, 497
– Riemann manifolds to Euclidean manifolds, 97
– sphere to cone, 379, 395
– sphere to cylinder, 19
– sphere to equatorial plane, 23, 33
– sphere to tangential plane, 23, 161
– sphere to torus, 92
Mars, 637, 655
matrix
– positive-definite, 2
– rotation, 8
– triangular, 507, 508, 511, 513, 517, 518
Maupertuis gauge, 543, 550
maximal angular distortion, 86
maximum angular distortion, 441–443
mean sea level, 637
mega data sets, 469
Hamilton equations, 428
Hamilton portrait, 416, 426, 428, 429, 431, 543, 546,
548
Hammer projection, 601
– ellipsoidal, 601, 616
– equiareal modified azimuthal, 33, 36
– retroazimuthal, 10
– – ID card, 10
Hasse diagram, 501–503
Hausdorff axiom of separation, 113
Hausdorff topological space, 113
Helmholtz differential equation, 61, 64
Hesse form, 37
Hesse matrix, 1, 81, 643
Hilbert invariants, 83
Hodge star operator, 102–104, 528
homeomorphism, 113, 114
Hooke matrices, 84
horizontal coordinate mean, 576
Hotine Oblique Mercator Projection (HOM), 113,
359
inclination, 132
indirect problem, 142
initial value problem, 426, 427, 429
initial values, 415
integrability conditions, 52
international reference ellipsoid, 113
inverse transformation, 151
Io, 637, 655
isometric, 48
isometric coordinates, see coordinates, conformal,
313, 316
isometric latitude, 264
isometry, 80
isoparametric mapping, 61
isothermal, 48
isothermal coordinates, see coordinates, conformal,
316
Jacobi matrix, 1, 5
Kartenwechsel, 11, 113, 454
Killing equations, 125
Killing symmetry, 126
Killing vectors, 113, 122–126, 129, 143
Korn–Lichtenstein equations, 43, 46, 48–51, 53,
55–57, 62, 64, 65, 97, 101, 313, 527
Krassowsky reference ellipsoid, 469
Kronecker delta, 361
Kronecker–Zehfuss product, 363
Lagrange function, 2
Lagrange multiplier, 2
Lagrange portrait, 416, 426, 428, 543, 546, 547
Lagrange projection, 161, 193
Lambert azimuthal, 391
Lambert conformal conic mapping, 405
Lambert conformal mapping, 409
Lambert cylindrical equal area projection, 276, 278
Lambert map, 161, 388
Lambert mapping, 379, 382, 386–388, 391, 405, 406,
409, 414
Lambert projection, 569
Laplace equation of harmonicity, 48
Laplace–Beltrami equations, 51–53, 55, 56, 62, 313,
325, 359–362, 529, 530
Laplace–Beltrami operator, 49, 50, 56, 64
least squares, 453, 460
left metric tensor, 7
Legendre recurrence, 416, 426–428, 434
Legendre series, see Legendre recurrence
length distortion, 11, see stretch
lexicographic order, 503
L’Hˆ opital Rule, 617
Lie recurrence, 416, 426, 429, 430, 433, 565
Lie series, see Lie recurrence
local datum, 469, 490
local reference system, 453
loxodrome, 273
mapping
– biaxial ellipsoid-of-revolution to sphere, 32
– concircular, 1
– conformal, 1, 32, 42, 43, 46, 48, 70, 72, 80, 83, 85,
86, 97, 101, 102, 105, 106, 221, 325, 359–361, 369,
406–409, 411–414, 497, 505, 519, 527
– conic, 405–407, 410, 414
– double projection, 32
– ellipsoid-of-revolution to cone, 405
– ellipsoid-of-revolution to cylinder, 313, 359
– ellipsoid-of-revolution to sphere, 2, 5, 39, 41, 53,
55, 62, 76, 83
– ellipsoid-of-revolution to tangential plane, 221
– equiareal, 1, 19, 20, 74, 76, 78, 79, 83, 85, 86, 111,
221, 406
– equidistant, 1, 42, 53, 55, 56, 75, 82, 83, 111, 221,
406, 411, 412, 414
– geodesic, 1
– geodetic, 415–417, 433, 439
– harmonic, 1
– isoparametric, 2–5, 7, 32, 39, 61, 70
– Jacobi, 4, 6
– loxodromic, 1
– mixed cylindric, 569, 589, 601, 637
– northern hemisphere to equatorial plane, 19, 33
– oblique orthogonal, 92, 93
– orthogonal, 19, 23, 28, 33–35, 92, 122, 638
– perspective, 221, 240
– pseudo-azimuthal, 10
– pseudo-cylindrical, 19, 589
– relation preserving, 497
– Riemann manifolds to Euclidean manifolds, 97
– sphere to cone, 379, 395
– sphere to cylinder, 19
– sphere to equatorial plane, 23, 33
– sphere to tangential plane, 23, 161
– sphere to torus, 92
Mars, 637, 655
matrix
– positive-definite, 2
– rotation, 8
– triangular, 507, 508, 511, 513, 517, 518
Maupertuis gauge, 543, 550
maximal angular distortion, 86
maximum angular distortion, 441–443
mean sea level, 637
mega data sets, 469