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| Rutherford D.E. — Vector methods. Applied to differential geometry, mechanics, and potential theory |
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| Предметный указатель |
Acceleration, components of 37 49 50
Angular velocity 47
Asymtotic lines, directions 33
Axis of dipole 89
Axis of magnet 83
Bernoulli’s equation 106
Bessel’s equation, functions 121
Binormal 18
Boscovitch’s hypothesis 45 58
boundary conditions 114 117 119
Canonical equations 23
Central Axis 42
Centrifugal force 50
Circulation 108
components 3
Conduction of heat 117
Conductor 97
Conservation of energy 57 130 131
Conservation of momentum 129
Conservative field 56
Continuity equation 105
Coordinates, curvilinear 26
Coordinates, cylindrical 72 121
Coordinates, orthogonal 70
Coordinates, spherical 72 118
Coriolis force 50
Coulomb’s law 83 100
Couple 40
Curl 63 124
Current 97
Curvature, average; Gaussian 31
Curvature, line of 30
Curvature, principal radius of 30
Curvature, radius of 21
Curvature, spherical 21
Curves, geometry of 16
Curvilinear integral 61
Dielectric 97
Dielectric, constant 99
Dipole 84 89
Dipole, distributions 90 91
Dipole, two-dimensional 92
Direction cosines 4
Displacement 99
distribution, 92
Distribution, due to a given, potential 114
Distribution, potential due to a given 88
Divergence 66 124
Doublet 84
d’Alembert’s principle 58
Electromagnetic equations 126
Electrostatic problem 116
Elliptical points 33
Energy, conservation of 57 130 131
Energy, kinetic 45 54
Energy, potential 56
Equipotential surfaces 93
Euler’s equations 52
Euler’s hydrodynamical equations 105
Euler’s theorem 33
Field of force 55
Field, line; tube 80
Field, vector 61
Fourier series 117
Frenet’s formulae 19
Fundamental quadratic forms 28 134
Fundamental quadratic forms, Gauss’s law 82
Gauss’s theorem 74
Gradient 60 124
Gravitation, Newton’s law of 83
Gravitational field 82
Green’s reciprocal theorem 76
Green’s Theorem 75
Heat, conduction of 117
Helix 23
Hyperbolic points 33
Insulator 97
Intensity 83 98
Intrinsic equations 22
Irrotational field 65
Kepler’s second law 49
Laplace’s equation 85 111
Laplace’s equation, special solutions of 117—120
Legendre’s equation, functions 118
Length of a vector 1
Line of curvature 30
Line, equation of a 11
Line, integral 61
Localised vector 38
Lorentz equations 126
Lorsntz transformation 129
Magnetic, particle 83
Magnetic, shell 91
Mass, centre 42
Mass, relative, rest 130
Meusnier’s theorem 30
| Moment of a couple 40
Moment of a magnet 83
Moment of a vector 38
Moment of inertia 51—54
Moment of momentum 44 45 51 54
Momentum 37 44
Momentum, conservation of 129
Momentum, moment of 44 45 51 54
Motion, equations of 37 46 52
Natural equations 22
Newton’s law of gravitation 83
Newton’s laws of 37 43
Newton’s laws of motion 37 43
Newton’s laws of, Moving axes 47—52
Newton’s laws of, Moving trihedral 19
Operator, “ ” 60 68 69
Operator, “\square” 124
Orthocentric tetrahedron 13
Osculating plane 17
Parabolic points 33
Paraboloid of revolution 34
Parallelogram law 1 37
Parametric lines 26
Pitch 42
Plane, equation of a 12
Poinsot’s central axis 42
Poisson’s equation 85
Polarisation 98
Position vector 11
Potential 78
Potential of a conductor 97
Potential, due to a dipole 89
Potential, due to a magnetic shell 91
Potential, due to a source 88
Potential, due to a vortex filament 108
Potential, due to special distributions 88—92
Potential, electrostatic 79
Potential, evaluation of 116—120
Potential, gravitational 79
Potential, magnetic 79
Potential, properties of 113
Potential, vector 96
Potential, velocity 79
Principal, axes 54
Principal, directions 30
Principal, normal 18
Products of inertia 51—54
Products of vectors 5—9 123 124
Relative mass 130
Relativity 126 129
Rest mass 130
Resultant 2
Scalar, product 5 123
Sink 81
Solenoidal 68
Source 81
Source, distributions 84 88
Source, strength 82
Source, two-dimensional 92
Stationary field 80
Steady field 80
Stokes’s theorem 74
Stream lines 80 102
Strength of a source 82
Strength of a tube 81
Sum of vectors 2
Surface, distributions 85 89
Surface, integral 65
Surfaces, geometry of 26
Tangent 17
Tangent, piano 27
Torsion 20
Triple products 8 9
Uniqueness theorem 112
Unit, binormal 19
Unit, line 81
Unit, principal normal 19
Unit, tangent 17
Unit, tube 81
Vector 1
Vector, field 61
Vector, localised 38
Vector, potential 96
Vector, product 6 124
Velocity, components of. 37 49
Velocity, potential 79
Velocity, vector 61 79 82 102
Virtual work 55
Volume distributions 84 88 90
Vortex lines 102
Vorticity 62 102 107
Wave equation 120
Work 55
World vector 123
Wrench 42
Zero vector 1
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