710 Index
de L’Isle mapping, 379, 382, 385
deformation, 4, 5
deformation measure, 1, 5, 36, 37, 74
– a review, 37
– additive, 75
– multiplicative, 5, 11
– scalar-valued, 84
– tensor-valued, 83
Deutsches Hauptdreiecksnetz, 485
diagonalization of symmetric matrices, 1, 2, 11, 14
diffeomorphism, 2, 4, 43, 74, 102, 103, 376, 611
dilatation factor, see stretch, 315
direct problem, 142
direct transformation, 148
dispersion matrix, 453, 467, 469
distortion analysis, 165
distortion energy, 37, 84, 85, 280–282, 445, 446
distortion energy density, 84
dynamic time, 543, 550
Earth, 33, 75, 82, 359, 417, 456, 638, 652, 655
Easting, 485, 486
Eckert II, 19–22, 299
Eckert mapping, 19
ellipsoid-of-revolution, 2, 3, 5, 32, 36, 39, 41, 53, 55,
56, 61, 62, 64, 70, 71, 76, 81, 83, 106–108, 110, 122,
125, 129, 143, 144, 221, 223, 225, 232, 234, 238,
240, 257, 262, 264, 269, 313, 316, 405, 415–418,
426, 437, 439, 569
– geodesic circle, 417
– geodesics, 415
– initial value problem, 433
– Taylor expansion, 429
ellipsoidal Hammer projection, 609
ellipsoidal isometric latitude, 55, 264
ellipsoidal Korn–Lichtenstein equations, 325
elliptic function, 519, 520, 524, 525
– addition theorem, 524
– periodicity, 524
– series expansion, 523
elliptic integral, 406, 519, 523–525
elliptic modulus, 519, 523
elliptic pseudo-cylindrical mapping, 293, 296
equal area mapping, 276, 278
equatorial frame of reference, 122–124, 126, 128–130
equatorial plane, 23, 33
equiareal azimuthal projection, 171, 173
equiareal mapping, 76, 106, 171, 225, 238
equidistant mapping, 82, 167, 225, 234, 276
Equidistant Polar Mapping (EPM), 166
equivalence theorem, 43, 74, 76, 79, 101
error propagation, 453, 467
erste geod¨ atische Hauptaufgabe, 565
Euler parameters, 248
Euler rotation matrix, 248
Euler–Lagrange deformation energy, 84
Euler–Lagrange deformation tensor, 29–34, 40, 41,
43, 74, 83, 84, 97, 99
Euler–Lagrange distortion energy, 85
exterior calculus, 102
factor of conformality, 51–53, 55, 56, 60–62, 64,
68–70, 527, 551
Fermi coordinates, 415, 417, 438, 439
fibering, 500
form parameters, 653, 655
Foucaut projection, 585
Frobenius matrix, 163
Frobenius norm, 2
fundamental form, 1
Gauss double projection, 257
Gauss–Krueger coordinates, 339, 416, 417, 440, 445,
446, 451, 469
Gauss–Krueger strip, 415
Gauss map, 644
Gauss projection, 61
Gauss surface normal latitude, 55, 62
Gauss surface normal longitude, 55, 62
Gauss–Weingarten equations, 543
Gauss–Krueger conformal coordinate system, 332
Gauss–Krueger conformal mapping, 325
Gauss–Krueger reference frame, 315
Gaussian curvature, 1, 56, 60, 61, 64, 68, 81, 153, 415
Gaussian curvature matrix, see Gaussian curvature
Gaussian differential invariant, 1
Gaussian factorization, 56
general eigenvalue–eigenvector problem, 2, 14
general eigenvalue problem, 13, 14, 29
general normal perspective mapping, 174, 177, 179,
185
general rotationally symmetric surfaces, 301
generalized Kepler equation, 589, 594
generalized Lambert projection, 569, 584
generalized Mollweide projection, 589
generalized Sanson–Flamsteed projection, 569, 584
geodesic circle, 417, 422, 424, 545
geodesics, 415, 416, 422, 428, 429, 543, 546, 551, 638
– Newton form, 546
geodesy
– three-dimensional, 637
geodetic curvature, 543
geodetic field of geodesics, 433
geodetic line, 434
geodetic mapping, 415
geodetic parallel, 434
geodetic parallel coordinates, 416
geodetic projection, 417, 433, 438
Geodetic Reference Figure, 313
Geodetic Reference System 1980, 222, 332, 342, 589
Geodetic Reference System 1984, 346, 354
geodetic torsion, 543
geoid, 637
geometric height, 637, 638
geometry space, 638
global datum, 469, 490
Global Positioning System (GPS), 113, 456, 469, 637
global reference system, 453
global rotation vector, 248
gnomonic projection, 161, 187
gravity vector, 248
Greenwich Meridian, 116, 119, 121, 138
Gr¨ obner basis, 637, 648
group, 360, 454
– conformal, 360, 363, 454
– special orthogonal, 454
de L’Isle mapping, 379, 382, 385
deformation, 4, 5
deformation measure, 1, 5, 36, 37, 74
– a review, 37
– additive, 75
– multiplicative, 5, 11
– scalar-valued, 84
– tensor-valued, 83
Deutsches Hauptdreiecksnetz, 485
diagonalization of symmetric matrices, 1, 2, 11, 14
diffeomorphism, 2, 4, 43, 74, 102, 103, 376, 611
dilatation factor, see stretch, 315
direct problem, 142
direct transformation, 148
dispersion matrix, 453, 467, 469
distortion analysis, 165
distortion energy, 37, 84, 85, 280–282, 445, 446
distortion energy density, 84
dynamic time, 543, 550
Earth, 33, 75, 82, 359, 417, 456, 638, 652, 655
Easting, 485, 486
Eckert II, 19–22, 299
Eckert mapping, 19
ellipsoid-of-revolution, 2, 3, 5, 32, 36, 39, 41, 53, 55,
56, 61, 62, 64, 70, 71, 76, 81, 83, 106–108, 110, 122,
125, 129, 143, 144, 221, 223, 225, 232, 234, 238,
240, 257, 262, 264, 269, 313, 316, 405, 415–418,
426, 437, 439, 569
– geodesic circle, 417
– geodesics, 415
– initial value problem, 433
– Taylor expansion, 429
ellipsoidal Hammer projection, 609
ellipsoidal isometric latitude, 55, 264
ellipsoidal Korn–Lichtenstein equations, 325
elliptic function, 519, 520, 524, 525
– addition theorem, 524
– periodicity, 524
– series expansion, 523
elliptic integral, 406, 519, 523–525
elliptic modulus, 519, 523
elliptic pseudo-cylindrical mapping, 293, 296
equal area mapping, 276, 278
equatorial frame of reference, 122–124, 126, 128–130
equatorial plane, 23, 33
equiareal azimuthal projection, 171, 173
equiareal mapping, 76, 106, 171, 225, 238
equidistant mapping, 82, 167, 225, 234, 276
Equidistant Polar Mapping (EPM), 166
equivalence theorem, 43, 74, 76, 79, 101
error propagation, 453, 467
erste geod¨ atische Hauptaufgabe, 565
Euler parameters, 248
Euler rotation matrix, 248
Euler–Lagrange deformation energy, 84
Euler–Lagrange deformation tensor, 29–34, 40, 41,
43, 74, 83, 84, 97, 99
Euler–Lagrange distortion energy, 85
exterior calculus, 102
factor of conformality, 51–53, 55, 56, 60–62, 64,
68–70, 527, 551
Fermi coordinates, 415, 417, 438, 439
fibering, 500
form parameters, 653, 655
Foucaut projection, 585
Frobenius matrix, 163
Frobenius norm, 2
fundamental form, 1
Gauss double projection, 257
Gauss–Krueger coordinates, 339, 416, 417, 440, 445,
446, 451, 469
Gauss–Krueger strip, 415
Gauss map, 644
Gauss projection, 61
Gauss surface normal latitude, 55, 62
Gauss surface normal longitude, 55, 62
Gauss–Weingarten equations, 543
Gauss–Krueger conformal coordinate system, 332
Gauss–Krueger conformal mapping, 325
Gauss–Krueger reference frame, 315
Gaussian curvature, 1, 56, 60, 61, 64, 68, 81, 153, 415
Gaussian curvature matrix, see Gaussian curvature
Gaussian differential invariant, 1
Gaussian factorization, 56
general eigenvalue–eigenvector problem, 2, 14
general eigenvalue problem, 13, 14, 29
general normal perspective mapping, 174, 177, 179,
185
general rotationally symmetric surfaces, 301
generalized Kepler equation, 589, 594
generalized Lambert projection, 569, 584
generalized Mollweide projection, 589
generalized Sanson–Flamsteed projection, 569, 584
geodesic circle, 417, 422, 424, 545
geodesics, 415, 416, 422, 428, 429, 543, 546, 551, 638
– Newton form, 546
geodesy
– three-dimensional, 637
geodetic curvature, 543
geodetic field of geodesics, 433
geodetic line, 434
geodetic mapping, 415
geodetic parallel, 434
geodetic parallel coordinates, 416
geodetic projection, 417, 433, 438
Geodetic Reference Figure, 313
Geodetic Reference System 1980, 222, 332, 342, 589
Geodetic Reference System 1984, 346, 354
geodetic torsion, 543
geoid, 637
geometric height, 637, 638
geometry space, 638
global datum, 469, 490
Global Positioning System (GPS), 113, 456, 469, 637
global reference system, 453
global rotation vector, 248
gnomonic projection, 161, 187
gravity vector, 248
Greenwich Meridian, 116, 119, 121, 138
Gr¨ obner basis, 637, 648
group, 360, 454
– conformal, 360, 363, 454
– special orthogonal, 454