Index
991
Total variation symbol, 99
Trace, 66
Trail, 66
Transformation, 387
Transposed tensor, 61
Transposition mirror image Hamiltonian
operator train, 730
Transposition of Hamiltonian operator train,
706
Transversality condition, 246, 260, 288, 378,
380
Trial function, 464
Triangle inequality, 389, 393
Tricomi problem, 453, 883
Trivial solution, 490
True motion, 516
True path, 516
Tubular field, 17
Two-dimensional Laplace operator, 412
Two-dimensional Laplacian operator, 412
U
Unbounded linear operator, 406
Unconstrained variational problem, 239
Undetermined boundary, 239
Undetermined endpoint, 239
Unfixed constraint, 515
Unfree particle system, 514
Unfree system, 514
Unilateral constraint, 515
Union, 385
Union of sets, 386
Union set, 386
Unitary operator, 408
Unit base vector, 10
Unit basis vector, 10
United Gauss formula, 40
United system of Euler equations, 177
Unit element, 392
Unit normal vector, 13
Unit operator, 405
Unit tensor, 61
Unit vector, 8, 10
Universal set, 386
Unsteady constraint, 515
Upper bound, 385
V
Vacant set, 385
Value field, 387, 404
Variable boundary, 239
Variable endpoint, 239
Variation, 98, 100, 104
Variational approach, 383
Variational calculus, 85
Variational condition, 96
Variational constraint condition, 96
Variational derivative, 114
Variational equation, 112
Variational integral, 101
Variational integrand, 101
Variational integrand function, 101
Variational methods, 85, 383
Variational notation, 98
Variational operator, 98
Variational principle, 85, 112, 383, 384, 513
Variational principle in mechanics, 513
Variational principle of mechanics, 513
Variational problem, 85
Variational problem of conditional
extremum, 319
Variational problem of undetermined
boundary, 239
Variational problem of variable boundary,
239
Variational problem with fixed endpoints, 95
Variational problem with fixed ends, 95
Variational symbol, 98
Variation of a curve, 244
Variation of a function, 98, 244
Variation of a functional, 104
Variation of a functional J[y(x)] aty=y(x),
110
Variation of a functional defined by
Lagrange, 110
Variation of a function F, 106
Variation of complementary strain energy,
544
Variation of coordinate, 553
Variation of density of complementary strain
energy, 544
Variation of strain energy, 520
Variation of strain energy density, 520
Variation of stress, 541
Variation principle, 85, 112, 383, 384, 513
Variation problem, 85
Varied path, 516
Variety of admissible curves, 95
Variety of admissible surfaces, 95
Variety of extremal curves, 115
Vector, 8, 59, 392
Vector differential operator, 10
Vector field, 8
Vector function, 8
Vector Laplace operator, 32
991
Total variation symbol, 99
Trace, 66
Trail, 66
Transformation, 387
Transposed tensor, 61
Transposition mirror image Hamiltonian
operator train, 730
Transposition of Hamiltonian operator train,
706
Transversality condition, 246, 260, 288, 378,
380
Trial function, 464
Triangle inequality, 389, 393
Tricomi problem, 453, 883
Trivial solution, 490
True motion, 516
True path, 516
Tubular field, 17
Two-dimensional Laplace operator, 412
Two-dimensional Laplacian operator, 412
U
Unbounded linear operator, 406
Unconstrained variational problem, 239
Undetermined boundary, 239
Undetermined endpoint, 239
Unfixed constraint, 515
Unfree particle system, 514
Unfree system, 514
Unilateral constraint, 515
Union, 385
Union of sets, 386
Union set, 386
Unitary operator, 408
Unit base vector, 10
Unit basis vector, 10
United Gauss formula, 40
United system of Euler equations, 177
Unit element, 392
Unit normal vector, 13
Unit operator, 405
Unit tensor, 61
Unit vector, 8, 10
Universal set, 386
Unsteady constraint, 515
Upper bound, 385
V
Vacant set, 385
Value field, 387, 404
Variable boundary, 239
Variable endpoint, 239
Variation, 98, 100, 104
Variational approach, 383
Variational calculus, 85
Variational condition, 96
Variational constraint condition, 96
Variational derivative, 114
Variational equation, 112
Variational integral, 101
Variational integrand, 101
Variational integrand function, 101
Variational methods, 85, 383
Variational notation, 98
Variational operator, 98
Variational principle, 85, 112, 383, 384, 513
Variational principle in mechanics, 513
Variational principle of mechanics, 513
Variational problem, 85
Variational problem of conditional
extremum, 319
Variational problem of undetermined
boundary, 239
Variational problem of variable boundary,
239
Variational problem with fixed endpoints, 95
Variational problem with fixed ends, 95
Variational symbol, 98
Variation of a curve, 244
Variation of a function, 98, 244
Variation of a functional, 104
Variation of a functional J[y(x)] aty=y(x),
110
Variation of a functional defined by
Lagrange, 110
Variation of a function F, 106
Variation of complementary strain energy,
544
Variation of coordinate, 553
Variation of density of complementary strain
energy, 544
Variation of strain energy, 520
Variation of strain energy density, 520
Variation of stress, 541
Variation principle, 85, 112, 383, 384, 513
Variation problem, 85
Varied path, 516
Variety of admissible curves, 95
Variety of admissible surfaces, 95
Variety of extremal curves, 115
Vector, 8, 59, 392
Vector differential operator, 10
Vector field, 8
Vector function, 8
Vector Laplace operator, 32