Index
985
Identity element, 392
Identity mapping, 388
Identity operator, 405
Ignorable coordinate, 554
Image, 387, 404
Image denoising functional, 637
Included in central field of extremal curve,
203
Included in extremal curve field, 203
Incompletely generalized variational principle, 384
Independent coordinates, 553
Independent function, 89
Indirect method in variational problem, 455
Indirect method of variational problem, 455
Indirect test for tensor character, 65
Inferior arc, 128
Infimum, 386
Infinite differentiable function, 90
Infinite set, 385
Inherent curve field, 201
Initial condition, 96
Injection, 387
Injective mapping, 387
Inner multiplication, 63
Inner point, 391
Inner product, 63, 394, 473
Inner product in domain, 473
Inner product on boundary, 473
Inner product space, 394, 395
Integrable differential constraint, 515
Integral constraint, 331
Integral curve, 115
Integral factor, 185, 427
Integral functional, 90
Integral type functional, 90
Integral variational principle, 513
Integral with parameter, 4
Integrating under the integral sign, 5
Interior, 392
Interior point, 391
Interior product, 63
Internal method, 473
Internal point, 391
Internal product, 63
Intersection, 386
Intersection set, 386
Invariance of differential form, 179
Invariance of Euler equation, 180
Invariant, 59
Invariant order operator, 695
Inverse element, 392
Inverse image, 388
Inverse mapping, 388
Inverse operator, 407
Inverse problem of variational problem, 383
Inverse symmetric tensor, 63
Inverse variational problem, 383
Invertible linear operator, 407
Invertible mapping, 387
Invertible operator, 407
Irremoval constraint, 515
Irrotational field, 29
Isochronal curve, 136
Isochronal variation, 99
Isochrone, 136
Isochronic curve, 136
Isochronous curve, 136
Isochronous variation, 99
Isolated point, 392
Isoline, 12
Isoline equation, 12
Isometric operator
Isomorphic mapping
Isomorphism
Isoperimetric condition, 89, 331
Isoperimetric constraint, 331
Isoperimetric problem, 89, 333
Isoplethic curve, 12
J
Jacobi accessory equation, 205
Jacobian determinant, 322
Jacobi condition, 208
Jacobi equation, 205
Jacobi operator, 412
Jacobi’s form of the principle of least action,
597
Jacobi strong condition, 208
Jaumann stress tensor, 702
Join, 385
K
Kantorovich method, 469
Kepler problem, 597, 604, 922
Kepler(’s) law of areas, 923
Kepler(’s) second law, 923
Kernel of a functional, 101
Kinematic constraint, 515
Kinetic boundary condition, 245
Kinetic energy density, 550
Kronecker delta, 52
Kronecker symbol, 52
985
Identity element, 392
Identity mapping, 388
Identity operator, 405
Ignorable coordinate, 554
Image, 387, 404
Image denoising functional, 637
Included in central field of extremal curve,
203
Included in extremal curve field, 203
Incompletely generalized variational principle, 384
Independent coordinates, 553
Independent function, 89
Indirect method in variational problem, 455
Indirect method of variational problem, 455
Indirect test for tensor character, 65
Inferior arc, 128
Infimum, 386
Infinite differentiable function, 90
Infinite set, 385
Inherent curve field, 201
Initial condition, 96
Injection, 387
Injective mapping, 387
Inner multiplication, 63
Inner point, 391
Inner product, 63, 394, 473
Inner product in domain, 473
Inner product on boundary, 473
Inner product space, 394, 395
Integrable differential constraint, 515
Integral constraint, 331
Integral curve, 115
Integral factor, 185, 427
Integral functional, 90
Integral type functional, 90
Integral variational principle, 513
Integral with parameter, 4
Integrating under the integral sign, 5
Interior, 392
Interior point, 391
Interior product, 63
Internal method, 473
Internal point, 391
Internal product, 63
Intersection, 386
Intersection set, 386
Invariance of differential form, 179
Invariance of Euler equation, 180
Invariant, 59
Invariant order operator, 695
Inverse element, 392
Inverse image, 388
Inverse mapping, 388
Inverse operator, 407
Inverse problem of variational problem, 383
Inverse symmetric tensor, 63
Inverse variational problem, 383
Invertible linear operator, 407
Invertible mapping, 387
Invertible operator, 407
Irremoval constraint, 515
Irrotational field, 29
Isochronal curve, 136
Isochronal variation, 99
Isochrone, 136
Isochronic curve, 136
Isochronous curve, 136
Isochronous variation, 99
Isolated point, 392
Isoline, 12
Isoline equation, 12
Isometric operator
Isomorphic mapping
Isomorphism
Isoperimetric condition, 89, 331
Isoperimetric constraint, 331
Isoperimetric problem, 89, 333
Isoplethic curve, 12
J
Jacobi accessory equation, 205
Jacobian determinant, 322
Jacobi condition, 208
Jacobi equation, 205
Jacobi operator, 412
Jacobi’s form of the principle of least action,
597
Jacobi strong condition, 208
Jaumann stress tensor, 702
Join, 385
K
Kantorovich method, 469
Kepler problem, 597, 604, 922
Kepler(’s) law of areas, 923
Kepler(’s) second law, 923
Kernel of a functional, 101
Kinematic constraint, 515
Kinetic boundary condition, 245
Kinetic energy density, 550
Kronecker delta, 52
Kronecker symbol, 52