982
Index
Density of virtual strain energy, 520
(de)numerable set, 388
Derivable, 415
Derived set, 392
Descending order operator, 695
Dido(’s) problem, 334
Difference, 386
Difference set, 386
Differentiable, 104
Differential constraint, 326, 515
Differential equation of motion, 528
Differential equations of equilibrium, 528
Differential operator, 14, 412
Differential variational principle, 513
Differentiating under the integral sign, 6
Differentiation under the integral sign, 6
Dirac constant, 634
Directional derivative, 9
Direction of principal axis, 65
Direct methods in variational problems, 455
Direct methods of variational problems, 455
Direct product, 387
Dirichlet boundary condition, 245
Dirichlet functional, 161
Dirichlet inner product, 396
Dirichlet integral, 161
Dirichlet problem, 161, 430, 457
Discrete spectrum, 490
Disjoint, 386
Displacement, 516
Displacement boundary, 529
Displacement of elastic body, 516
Displacement vector, 516
Distance, 389
Distance axioms, 389
Distance of n-th order, 92
Distance space, 389
Distance structure, 389
Divergence, 16, 23
Divergence theorem, 20
Divergence type functional, 654
Domain, 91, 387, 400, 404
Domain of definition, 91, 387, 404
Dot product, 63
Driving function, 419
Duality principle, 343
Dual space, 408
Du Bois-Reymond lemma, 49
Dummy index, 51
Dyad, 63
E
E-function, 214
Eigenelement, 490
Eigenequation, 490
Eigenfunction, 490
Eigenspectrum, 490
Eigenvalue, 65, 490, 852
Eigenvalue problem, 490
Eigenvector, 490
Einstein summation convention, 51
Elastic body, 516
Elasticity, 516
Elastic system, 516
Electromagnetic field problem, 628
Element, 384
Elementary work, 518
Empty set, 385
Energy functional, 384
Energy integral, 383, 384
Energy method, 384, 513
Energy norm, 396
Energy of deformation, 519, 521
Energy principle, 513
Enumerable set, 388
Epimorphism, 387
Epsilon-delta (ε-δ) identity, 55
Equality, 61, 386
Equation of motion, 528
Equation of strain compatibility, 518
Equation of virtual work, 526, 533
Equations of equilibrium, 528
Equipollence, 388
Equipotent
Equivalence, 388
Equivalent, 388
Erdmann(’s) first corner condition, 297
Erdmann(’s) second corner condition, 297
Ericksen’s reduced energy functional, 638
Ericksen’s simplified energy functional, 638
Essential boundary conditions, 245
Euclidean norm, 393, 394
Euclidean space, 394
Euler equations, 113, 118, 147, 159, 177
Euler-Lagrange(’s) equation, 114
Euler-Poisson(’s) equation, 147
Euler(’s) homogeneous function theorem,
367
Exterior, 392
Exterior point, 391
Exterior product, 63
External point, 391
External product, 63
Extremal, 95, 115
Extremal curve, 95, 115
Extremal curve field, 201, 203
Index
Density of virtual strain energy, 520
(de)numerable set, 388
Derivable, 415
Derived set, 392
Descending order operator, 695
Dido(’s) problem, 334
Difference, 386
Difference set, 386
Differentiable, 104
Differential constraint, 326, 515
Differential equation of motion, 528
Differential equations of equilibrium, 528
Differential operator, 14, 412
Differential variational principle, 513
Differentiating under the integral sign, 6
Differentiation under the integral sign, 6
Dirac constant, 634
Directional derivative, 9
Direction of principal axis, 65
Direct methods in variational problems, 455
Direct methods of variational problems, 455
Direct product, 387
Dirichlet boundary condition, 245
Dirichlet functional, 161
Dirichlet inner product, 396
Dirichlet integral, 161
Dirichlet problem, 161, 430, 457
Discrete spectrum, 490
Disjoint, 386
Displacement, 516
Displacement boundary, 529
Displacement of elastic body, 516
Displacement vector, 516
Distance, 389
Distance axioms, 389
Distance of n-th order, 92
Distance space, 389
Distance structure, 389
Divergence, 16, 23
Divergence theorem, 20
Divergence type functional, 654
Domain, 91, 387, 400, 404
Domain of definition, 91, 387, 404
Dot product, 63
Driving function, 419
Duality principle, 343
Dual space, 408
Du Bois-Reymond lemma, 49
Dummy index, 51
Dyad, 63
E
E-function, 214
Eigenelement, 490
Eigenequation, 490
Eigenfunction, 490
Eigenspectrum, 490
Eigenvalue, 65, 490, 852
Eigenvalue problem, 490
Eigenvector, 490
Einstein summation convention, 51
Elastic body, 516
Elasticity, 516
Elastic system, 516
Electromagnetic field problem, 628
Element, 384
Elementary work, 518
Empty set, 385
Energy functional, 384
Energy integral, 383, 384
Energy method, 384, 513
Energy norm, 396
Energy of deformation, 519, 521
Energy principle, 513
Enumerable set, 388
Epimorphism, 387
Epsilon-delta (ε-δ) identity, 55
Equality, 61, 386
Equation of motion, 528
Equation of strain compatibility, 518
Equation of virtual work, 526, 533
Equations of equilibrium, 528
Equipollence, 388
Equipotent
Equivalence, 388
Equivalent, 388
Erdmann(’s) first corner condition, 297
Erdmann(’s) second corner condition, 297
Ericksen’s reduced energy functional, 638
Ericksen’s simplified energy functional, 638
Essential boundary conditions, 245
Euclidean norm, 393, 394
Euclidean space, 394
Euler equations, 113, 118, 147, 159, 177
Euler-Lagrange(’s) equation, 114
Euler-Poisson(’s) equation, 147
Euler(’s) homogeneous function theorem,
367
Exterior, 392
Exterior point, 391
Exterior product, 63
External point, 391
External product, 63
Extremal, 95, 115
Extremal curve, 95, 115
Extremal curve field, 201, 203