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| Aristotle D. Michal — Matrix and tensor calculus: with applications to mechanics, elasticity, and aeronautics |
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| Предметный указатель |
Aircraft flutter, calculation of 34 35 36
Aircraft flutter, description of 32
Aircraft flutter, matric differential equation of 33
Aircraft flutter, need for matric theory in calculations for fast aircraft 37
Aitken 124
Appell 125
Bingham 14 124
Biot 34 113 124
Bleakney 124
Bocher 111 124
Born 111 124
Boundary layer, theory of Prandtl 109
Boundary layer, thickness of 109
Boundary-layer equations 104 105 106 107 108
Brillouin 117 125
Carslaw 34 124
Cartan 121
Cayley — Hamilton theorem for matrices 12
Chien x 105 127
Christopfel symbols, Euclidean 53
Christopfel symbols, multidimensional Euclidean 95
Christopfel symbols, proof of law of transformation of 114 115
Christopfel symbols, Riemannian 96
Codazzi equations for a surface 122
Collar 1 34 35 124
Compressible fluids 103 104
Contraction of a tensor 116
Correlation tensor field in turbulence 73 74
Cosserat, E. and F. 117
Covariant differentiation of Euclidean metric tensor 59
Covariant differentiation of scalar field 60
Covariant differentiation of tensor fields in general 58
Covariant differentiation of vector fields 56 57
Covariant differentiation, its commutativity in Euclidean spaces 58 59
Covariant differentiation, its non-commutativity in general in Riemannian spaces 99 100
Cramer's rule 111
Crystalline media 93
Curvature of a surface, Gaussian 123
Curvature of a surface, mean 123
Darboux 126
Den Hartog 124
Differential equations of small oscillations 24 25
Differential equations with variable coefficients 21 22
Differential equations, example 25 26
Differential equations, frequencies and amplitudes 29 30 31
Differential equations, harmonic solutions 28
Differential equations, solution of linear 20
Differentiation of matrices 16
Dirac 111 124
Duncan 1 34 35 124
Dynamical systems with n degrees of freedom 24 101
Dynamical systems with n degrees of freedom, Lagrange's equations of motion of 24 101
Eisenhart 118 126
Elastic deformation, change in volume under 79 80 81
Elastic deformation, matrix methods in formulation of finite 38 39 40
Elastic deformation, tensor methods in formulation of finite 75 76 77
Elastic potential 91 92
Equation of continuity 69 70 71 103
Ertel 114 116 126
Euclidean Christoffel symbols 53
Euclidean Christoffel symbols for Euclidean plane 54
Euclidean Christoffel symbols, alternative form for 54
Euclidean Christoffel symbols, exercise on 55
Euclidean Christoffel symbols, law of transformation of 53
Euclidean Christoffel symbols, multidimensional 95
Euclidean metric tensor 43
Euclidean metric tensor, exercises on 47
Euclidean metric tensor, its law of transformation 46
Euclidean spaces 42
Euclidean spaces, multidimensional 95
Euler — Lagrange equations for geodesics 100
Eulerian strain tensor 77 78
Fantappie 112 124
Fluids, compressible 103 104
Fluids, incompressible 103 104
Fluids, incompressible, boundary-layer equations for 104 105 106
Fluids, Navier — Stokes equations for incompressible viscous 104
Fluids, Navier — Stokes equations for viscous 69 70
Frazer 1 34 35 124
Functionals 18 112
Fundamental forms of a surface 122
Garrick 36 125
Gauss 43
Gauss, equations for a surface 122
General theory of relativity 42
Geodesic coordinates 97
Geodesics 100
Geodesics, dynamical trajectories as 118 119 120 121
Geodesics, Euler — Lagrange equations for 100
Goursat 118 121
Holzer 124
Homogeneous strains 83
Homogeneous strains, fundamental theorem on 84 85 86
Hooke's law 94
Hotelling 111 124
Howarth 126
Hydrodynamics 42
Hydrodynamics, Eulerian equations 116
Hydrodynamics, Lagrangean equations 116
Integral invariants 121
Isotropic medium 92 93 94
Isotropic medium, condition for 92 93
Isotropic medium, stress-strain, relations for 93 94
Isotropic strain 84
Jaeger 34 124
Jeffreys 126
JORDAN 111 124
Karman x 34 38 74 113 124 126
Kasner 126
Killing's differential equations 88
Kinetic potential 101
Kirchhoff 117 126
Kussner 124
Lagrange's equations of motion 24 201 102
Lagrangean strain tensor 77 78
Lamb 116 126
Laplace equation 62 63
Laplace equation for vector fields 65
Laplace equation in curvilinear coordinates 63 64
Levi-Civita 117 127
LIB 121
Libber ix 124 125
Lie x 104 105
Line element 42
Line element in curvilinear coordinates 45 46 47
Line element, exercises on 45 46 47
Line element, geodesic form of 105
Line element, Riemannian 96
Linear algebraic equations, solutions 9
| Linear algebraic equations, solutions, numerical 14
Linear algebraic equations, solutions, punched-card methods 14
Linear differential equations in matrices 21 22
Linear differential equations with constant coefficients 20
Linear differential equations with variable coefficients 21 22
Linear differential equations, application of matric exponential to 20
Linear differential equations, method of successive substitutions in solution of 22
Lipp ix
Love 126
MacDuffee 125
Martin 112 125
Matric exponential, application to systems of linear differential equations with constant coefficients 20
Matric exponential, convergence of 112
Matric exponential, definition of 15
Matric exponential, properties of 16
Matric power series, definition of 15
Matric power series, theorem on computation of 18
Matrix of same type 2
Matrix, addition 2
Matrix, adjoint of 39
Matrix, application of inverse, to solution of linear algebraic equations 9
Matrix, Cayley — Hamilton theorem 12
Matrix, characteristic equation of 12
Matrix, characteristic function of 12
Matrix, characteristic roots of 12
Matrix, column 2
Matrix, definition of 1
Matrix, differentiation of, with respect to numerical variable 16
Matrix, dynamical 29
Matrix, example of non-commutativity of matrix multiplication 5
Matrix, index and power laws 11
Matrix, integration of, with respect to numerical variable 17
Matrix, inverse 8
Matrix, multiplication 5
Matrix, multiplication by number 11
Matrix, norm of 112
Matrix, order 2
Matrix, polynomials in a 11
Matrix, row 2
Matrix, rule for computation of inverse 13
Matrix, square 2
Matrix, strain 39 40 41
Matrix, symmetric 40
Matrix, trace of 13 111
Matrix, unit 4
Matrix, zero 3
McConnell 122 126
Michal ix x 112 114 116 118 121 125 126
Millikan x
Multiple-point tensor fields 71 72 73 74
Multiple-point tensor fields in elasticity theory 76
Multiple-point tensor fields in Euclidean geometry 71 72 73 74
Multiple-point tensor fields in turbulence 73 74
Murnaghan 117 126
Navier — Stokes differential equations for a viscous fluid 69
Navier — Stokes differential equations in curvilinear coordinates 70
Navier — Stokes differential equations subject to condition of incompressibility 104
Norm of a matrix 112
Normal coordinates 116
Normed linear ring 112
Oldenburger 125
Pipes 125
Plastic deformation 114
Poincare 121
Poisson equation 66 67 68
Principal radii of curvature of boundary-layer surface 108
Putt ix
Quadratic differential form 45 46
Reutter 127
Ricci 117 127
Riemann 127
Riemann — Christoffel curvature tensor 99 100
Riemannian geometry 96 97 98 99 100
Riemannian geometry, applications to boundary-layer theory 103 104 105 106 107 108 109 110 121 123
Riemannian geometry, applications to classical dynamics 101 102
Riemannian geometry, example 98
Riemannian geometry, infinite dimensional, x 118
Rigid displacement 40 77
Scalar density 60 61 67
Scalar field 49
Scalar field, relative 60 61 62
Schwarz 124
Strain invariant 82 117 118
Strain matrix 39 40 41
Strain matrix in infinitesimal theory 41
Strain tensor 48 49
Strain tensor, Eulerian 77
Strain tensor, Lagrangean 77
Strain tensor, variation of 86 87 88
Stress tensor 89 90
Stress tensor, symmetry of 91
Stress vector 89 90
Stress-strain relations for isotropic medium 93 94
Summation convention 4 43
Sylvester's theorem 112 113
Synge 127
Tensor analysis 56
Tensor analysis in multidimensional Euclidean spaces 95
Tensor analysis in Riemannian spaces 97 99 100
Tensor analysis, applications to boundary-layer theory 103 104 105 106 107 108 109 110 121 122 123
Tensor analysis, applications to classical dynamics 101 102 118 119 120 121
Tensor field of rank two, contravariant 50
Tensor field of rank two, covariant 50
Tensor field of rank two, mixed 50
Tensor field, contraction of a 116
Tensor field, covariant differentiation of 57 58
Tensor field, exercises on 59
Tensor field, general definition of 57 58
Tensor field, property of a 59
Tensor field, relative 60 117
Tensor field, Riemann — Christoffel curvature 99 100
Tensor field, weight of 60
Theodorsen 33 36 125
Thomas 114 116 118 126 127
Timoshenko 125
Turbulence 73 74
Turbulence, correlation tensor field in 73 74
Veblen 114 127
Vector field in rectangular cartesian coordinates 50
Vector field, contravariant 49
Vector field, covariant 49
Velocity field 51
Velocity field, divergence of 103 117
Volterra 112 125
Wave equation 65 66
Webster 116 127
Wedderburn 125
Whitehead 114 127
Whittaker 28 125 127
Wright 127
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