984
Index
Gauss theorem of electric field, 630
Gauss theorem of magic field, 630
General constraint condition, 96
General elliptic (differential) equation, 430
General equation of dynamics, 547
Generalized complementary energy, 589,
594
Generalized coordinates, 553
Generalized form of Hamilton(’s) principle,
549
Generalized functional, 344, 588
Generalized isoperimetric problem, 333
Generalized Levinson principle, 701
Generalized momentum, 554, 582
Generalized potential energy, 590, 594
Generalized variational principle, 384
Generalized variational problem, 345
Generalized velocity, 554
Generalized Veubeke principle, 702
Geodesic, 88
Geodesic line, 88
Geodesic line problem, 88, 328
Geometrical constraint, 320, 515
Geometrical equations, 517
Geometric boundary conditions, 245
Gibbs free energy functional, 635
Ginzburg-Landau energy functional, 703
Ginzburg-Landau equations, 636
Global extremum, 96
Global extremum function, 96
Global maximum, 96
Global maximum function, 96
Global minimum, 96
Global minimum function, 96
Gradient, 10, 415
Gradient field, 14
Gradient formula, 27
Gradient operator, 412
Gradient theorem, 27
Gradient type functional, 641
Gradient vector flow, 638
Great circle, 128
Greatest lower bound, 386
Green(’s) first formula, 24
Green(’s) first theorem, 24
Green(’s) first vector formula, 83, 760
Green(’s) formulas, 23, 520
Green(’s) second formula, 25
Green(’s) second theorem, 25
Green(’s) second vector formula, 83, 760
Green(’s) theorem, 23
Green(’s) third formula, 25
Green(’s) third theorem, 25
H
Hamiltonian, 10, 412
Hamiltonian equations, 582
Hamiltonian form, 581
Hamiltonian function, 581
Hamiltonian operator, 10, 412, 635
Hamiltonian operator string, 706
Hamiltonian operator train, 706
Hamiltonian variable, 582
Hamilton operator, 10, 412, 635
Hamilton(’s) action, 549
Hamilton(’s) canonical equations, 582
Hamilton(’s) equations, 582
Hamilton(’s) principle, 549
Harmonic field, 32
Harmonic function, 32
Harmonic operator, 19
Harmonic quantity, 32
Hellinger-Reissner generalized variational
principle, 587
Hellinger-Reissner principle, 587
Hellinger-Reissner variational principle, 587
Helmholtz equation, 637
Hermite equation, 423
Hermite operator, 408
Hermitian operator, 408
Hilbert adjoint operator, 408
Hilbert inner product, 395
Hilbert invariant integral, 212
Hilbert space, 397
Hölder inequality, 70
Hölder norm, 394
Holonomic constraint, 320, 515
Holonomic system, 515
Homogeneity, 393, 394
Homogeneous boundary condition, 404
Homogeneous equation, 404
Homogeneous function, 366
Homogeneous function of order n, 366
Homogeneous operator, 405
Hu Haichang-Kyuichiro Washizu generalized variational principle, 590, 700
Hu Haichang-Kyuichiro Washizu variational
principle, 590
Hu-Washizu principle, 590
Hypergeometric differential equation, 423
I
Ideal constraint, 547
Idealized constraint, 547
Identification of Lagrange multiplier, 320
Identifying Lagrange multiplier, 320
Identity, 389
Index
Gauss theorem of electric field, 630
Gauss theorem of magic field, 630
General constraint condition, 96
General elliptic (differential) equation, 430
General equation of dynamics, 547
Generalized complementary energy, 589,
594
Generalized coordinates, 553
Generalized form of Hamilton(’s) principle,
549
Generalized functional, 344, 588
Generalized isoperimetric problem, 333
Generalized Levinson principle, 701
Generalized momentum, 554, 582
Generalized potential energy, 590, 594
Generalized variational principle, 384
Generalized variational problem, 345
Generalized velocity, 554
Generalized Veubeke principle, 702
Geodesic, 88
Geodesic line, 88
Geodesic line problem, 88, 328
Geometrical constraint, 320, 515
Geometrical equations, 517
Geometric boundary conditions, 245
Gibbs free energy functional, 635
Ginzburg-Landau energy functional, 703
Ginzburg-Landau equations, 636
Global extremum, 96
Global extremum function, 96
Global maximum, 96
Global maximum function, 96
Global minimum, 96
Global minimum function, 96
Gradient, 10, 415
Gradient field, 14
Gradient formula, 27
Gradient operator, 412
Gradient theorem, 27
Gradient type functional, 641
Gradient vector flow, 638
Great circle, 128
Greatest lower bound, 386
Green(’s) first formula, 24
Green(’s) first theorem, 24
Green(’s) first vector formula, 83, 760
Green(’s) formulas, 23, 520
Green(’s) second formula, 25
Green(’s) second theorem, 25
Green(’s) second vector formula, 83, 760
Green(’s) theorem, 23
Green(’s) third formula, 25
Green(’s) third theorem, 25
H
Hamiltonian, 10, 412
Hamiltonian equations, 582
Hamiltonian form, 581
Hamiltonian function, 581
Hamiltonian operator, 10, 412, 635
Hamiltonian operator string, 706
Hamiltonian operator train, 706
Hamiltonian variable, 582
Hamilton operator, 10, 412, 635
Hamilton(’s) action, 549
Hamilton(’s) canonical equations, 582
Hamilton(’s) equations, 582
Hamilton(’s) principle, 549
Harmonic field, 32
Harmonic function, 32
Harmonic operator, 19
Harmonic quantity, 32
Hellinger-Reissner generalized variational
principle, 587
Hellinger-Reissner principle, 587
Hellinger-Reissner variational principle, 587
Helmholtz equation, 637
Hermite equation, 423
Hermite operator, 408
Hermitian operator, 408
Hilbert adjoint operator, 408
Hilbert inner product, 395
Hilbert invariant integral, 212
Hilbert space, 397
Hölder inequality, 70
Hölder norm, 394
Holonomic constraint, 320, 515
Holonomic system, 515
Homogeneity, 393, 394
Homogeneous boundary condition, 404
Homogeneous equation, 404
Homogeneous function, 366
Homogeneous function of order n, 366
Homogeneous operator, 405
Hu Haichang-Kyuichiro Washizu generalized variational principle, 590, 700
Hu Haichang-Kyuichiro Washizu variational
principle, 590
Hu-Washizu principle, 590
Hypergeometric differential equation, 423
I
Ideal constraint, 547
Idealized constraint, 547
Identification of Lagrange multiplier, 320
Identifying Lagrange multiplier, 320
Identity, 389