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Logan J.D. Invariant Variational Principles
Logan J.D.  Invariant Variational Principles









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: Invariant Variational Principles

: Logan J.D.

: en

: /

:

ed2k: ed2k stats

: 1977

: 172

: 02.07.2008

: | | ID
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Absolute invariance of higher-order integrals      117118 122
Absolute invariance of multiple integrals      64
Absolute invariance of single integrals      3034
action      11
Action integral for dynamical systems      12
Action integral for electrodynamics      104
Action integral for multiple integral problems      17 113
Action integral for physical fields      92
Action integral for single integral problems      5 113
Adjoint operator      159
Admissible function      1
Angular momentum tensor      96
Arclength      33 151
Brachistochrone problem      26
Canonical momentum      37 38 73 121
Center of mass      46 47
Configuration space      10
Conformal factor      133
Conformal invariance      158161
Conformal point transformation      132
Conformal transformation of metric tensor      133
Conservation law      22 37 7074
Conservation of angular momentum      44 97
Conservation of energy      3738 42 9697 100 107 109 120121
Conservation of linear momentum      42
contravariance      79
Covariance      79
Covariance, conformal      145147
Degree of contravariance      79
Degree of contravariance of covariance      79
Dilation      131 135 139140 146
Dilation, infinitesimal generators for      140
Dilation, invariance under      141143
Divergence theorem      16
Divergence-invariance      34
Divergence-invariance for n-body problem      44 45
Dual vector space      79 80
Electric field intensity      99
electromagnetic field      93 98104 107109 146147 160
Electromagnetic field, tensor      103
Electromagnetic potential      see Four-potential
Emdens equation      52
Energy      see Conservation of energy
Energy, electric      99
Energy, magnetic      99
Energy-momentum tensor      108
Euler equations      see Euler Lagrange equations
Euler expressions for multiple integrals      21
Euler expressions for second-order problems      115 119 124
Euler expressions for single integrals      10 36 159 161
Euler Lagrange equations for dynamical systems      20
Euler Lagrange equations for higher-order problems      128
Euler Lagrange equations for multiple integrals      12
Euler Lagrange equations for physical fields      9293
Euler Lagrange equations for second-order problems      112117
Euler Lagrange equations for single integrals      7
Euler Lagrange expressions      see Euler expressions
Eulers theorem      143
Extremal      8
Extremal surface      21
Fermats principle      11 50
Field equations      21 92
Field functions      92
Field, scalar      77 82
Field, tensor      8182
Field, vector      77
First integrals      8 27 37 120121
First integrals for n-body problem      3937
Four-potential      93 101
Functional      1
Fundamental integral      see Action integral
Fundamental invariance identities for higher-order problems      128
Fundamental invariance identities for multiple integrals      66
Fundamental invariance identities for second-order problems      118 122
Fundamental invariance identities for single integrals      34 52
Fundamental lemma of calculus of variations for multiple integrals      19
Fundamental lemma of calculus of variations for single integrals      6
Fundamental variational formula      23 162
Galilean invariance      41 77
Galilean transformations      41 76
Gauge transformation      102 160
Generators      29 63
Group, Galilean      41
Group, general Lorentz      85
Group, inhomogeneous Lorentz      86
Group, Poincare      86 88 93
Group, proper Lorentz      86 89
Group, r-parameter local Lie      28
Group, special conformal      138139
Hamiltonian      37 107
Hamiltonian complex      73
Hamiltons principle      11 14
Homogeneous function      143
Inertial frame      76
Infinitesimal generator      see Generators
Infinitesimal transformation      89
Invariance identities      see Fundamental invariance identities
Invariance of action integral      see Absolute invariance
Invariance problems      2 22
Invariant      see Absolute invariance
Inverse problem      59
Involution      136
Jacobi matrix      78
Jacobian      78
Killings equations      55
Killings equations, generalized      56
Kinctic energy      II 13
Klein Gordon equation      92 97 149
Korteweg de Vries equation      7475 124
Korteweg de Vries equation, conservation laws for      7475 126127
Lagranges equations      see Euler Lagrange equations
Lagrangian      4 11 16
Lagrangian density      92
Lagrangian for area of surface of revolution      9
Lagrangian for brachistochrone problem      26
Lagrangian for central force field      38
Lagrangian for damped harmonic oscillator      5657
Lagrangian for electromagnetic field      101 104
Lagrangian for harmonic oscillator      12
Lagrangian for Klein Gordon equation      97
Lagrangian for Korteweg de Vries equation      125
Lagrangian for n-body problem      13 40
Lagrangian for Plateaus problem      21
Lagrangian for vibrating rod      116
Lagrangian for wave equation      64
Laplacian operator      92
Liouvilles theorem      136 138
Lorentz condition      102
Lorentz transformation      86
Lorentz transformation, general      84
Lorentz transformation, infinitesimal      90
Lorentz transformation, proper      86
Magnetic deflection      99
Manifold      78
Maupertuis principle      11
Maxwell stress tensor      109
Maxwells equations      93
Maxwells equations in tensor form      104
Maxwells equations in vector form      100
Metric tensor      92
Minimum, absolute      1
Minimum, relative      1 3
Minkowski metric      91
n-body problem      13 14 39
Necessary conditions for an extremum      1
Necessary conditions for an extremum for functionals      3
Necessary conditions for an extremum for second-order problems      112115
Necessary conditions for an extremum, multiple integral problems      20
Necessary conditions for an extremum, single integral problems      7
Noethers identities      see Noethers theorem
Noethers theorem      22
Noethers theorem for higher-order multiple integrals      123
Noethers theorem for higher-order single integrals      119
Noethers theorem for infinite continuous groups      158161
Noethers theorem for multiple integrals      67
Noethers theorem for single integrals      36
Norm      2
Norm, weak      4
Normal region      15
Normed linear space      2
Parameter-invariant      150
Pendulum      4950
Plateaus problem      21
Poincare group      see Group
Poynting vector      100 109
Rotation of plane      29
Rotation, infinitesimal      29 139
Rotation, spatial      41 135
Scalar field      77 82 92 9598 139145
Scalar field, conformal invariance identities      140143
Scalar field, conservation laws for      9596 144145
Scalar field, general invariance identities      9798
Scalar potential      see Four-potential
Second Noether theorem      158161
Smith Hemholtz invariant      50
Snells law      50
Special conformal transformation      138139
Stationary      8
Sufficient conditions for parameter-invariance      153155
Summation convention      6
Surface of revolution      9
Tensor operations, contraction      81
Tensor operations, product      80
Tensor operations, raising and lowering indices      82 83
Tensor operations, sum      110
Tensors      7983
Tensors, rank of      79
Tensors, transformation law for      79
Transformation, r-parameter family      28
Translation, space      41
Translation, space-time      93
Translation, time      41
Variation, first      3
Variation, Gateaux      3
Variation, weak      3
Variational integral      see Action integral
Vector field      77 82 92 105107 145147
Vector field, conservation laws for      106 145147
Vector potential      see Four-potential
Vector, contravariant      81
Vector, covariant      81
Vector, timelike      109
Velocity transformations      41 76
Wave equation      65 93 111
Weierstrass representation      156157 161
Zermelos condition      155157
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