Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Zelikin M.I. — Control Theory and Optimization, Vol. 1
Zelikin M.I. — Control Theory and Optimization, Vol. 1

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Control Theory and Optimization, Vol. 1

Автор: Zelikin M.I.

Аннотация:

This book is devoted to geometric methods in the theory of differential equations with quadratic right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. Connections of the calculus of variations and the Riccati equation with the geometry of Lagrange-Grassmann manifolds and classical Cartan-Siegel homogeneity domains in a space of several complex variables are considered. The book is addressed to undergraduate and graduate students, scientific researchers and all specialists interested in the problems of geometry, the calculus of variations, and differential equations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 284

Добавлена в каталог: 09.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\phi$-compatible functions      85
$\phi$-compatible vector fields      85
Absolute      11 175
Adjoint representation of Lie algebras      92
Adjoint representation of Lie groups      92
Base of a fiber bundle      217
Basis forms of a distribution      220
Bellman equation      67
Bundle, canonical      218
Bundle, fiber of      217
Bundle, normal      50 218
Bundle, principal      199
Bundle, section of      219
Bundle, tangent      218
Bundle, vector (linear)      217
Canonical system of equations      16
Center of a Lie algebra      96
Chain rule      191
Clifford algebra      135
Clifford translation      152
Closed function      14
Commutator      86
Complexified matrix Riccati equation      187
Condition, Hilbert      15
Condition, Jacobi      30
Condition, Jacobi, strengthened      30
Condition, Legendre      26
Condition, Legendre — Caratheodory      252
Condition, Legendre — Weyl      242
Condition, strengthened Legendre      27
Condition, transversality      19
Condition, Weierstrass — Erdman      22
Conjugate point      28
Conjugating matrix      245
Connection, flat      235
Connection, general, on a bundle      227
Connection, linear      228
Connection, Riemannian (Levi — Civita)      231
Connection, symmetrical      230
Coordinates, conformal      209
Coordinates, matrix affine      264
Coordinates, matrix homogeneous      264
Coordinates, Plucker      115
Covariant derivative      230
Covering path      228
Cristoffel symbols      12 233
Curvature of connection      234
Curve, horizontal      227
Curve, modular      176
Curve, with scalar double ratio      143
Dirichlet functional      236
Dirichlet integral      210
distribution      220
Distribution, completely integrable      224
Distribution, involutive      222
Distribution, smooth      220
Double ratio      3
Equation, Bellman      67
Equation, Euler      7 214
Equation, Euler — Jacobi      215
Equation, Hamilton — Jacobi      24
Equation, Riccati      2
Equation, Riccati, complexified matrix      187
Equation, Riccati, matrix      31 61
Equation, Riccati, partial differential      260
Equation, Schwartz      203
Equation, variation      216
Euler equation      7 214
Euler — Jacobi equation      215
Exponential mapping      101
Exterior covariant differential      235
Fiber of a bundle      217
Field, Jacobi      216
Field, of extremals      53
Field, of extremals, $\phi$-compatible vector      85
Field, potential      270
Field, vector      85
Field, vector, covariantly constant      232
Field, vector, left-invariant      86
Flow on the homogeneity domain of type I      192
Flow on the homogeneity domain of type II      194
Flow on the homogeneity domain of type IV      196
Focal point      42 55
Foliation      222
Foliation, Reeb      223
Form, basis, of a distribution      220
Form, connection      229
Form, contact      244
Form, curvature      235
Form, differential      45
Form, Killing      93
Form, Poincare — Cartan      18
Form, quadratic, for determination of angles      134
Fourth harmonic      147
Function, $\phi$-compatible      85
Function, closed      14
Function, Weierstrass      44
Generalized unit disk      172
Geodesic      9
Geodesic inclination of a field      53 241
Geodesic symmetry      102
Geodesic symmetry with respect to a manifold      147
Group, fundamental      198
Group, Lie      80
Group, linear (matrix)      80
Group, linear (matrix) simple      96
Group, linear (matrix), semisimple      96
Group, structure, of a fiber bundle      217
Haar measure      98
Half-plane, generalized Siegel upper      177
Half-plane, Klein — Poincare      174
Half-plane, Lobachevsky      10
Hamilton — Jacobi equation      24
Hilbert condition      15
Hilbert invariant integral      54
Homogeneity (Cartan — Siegel) domain      166
Homogeneity (Cartan — Siegel) domain of type I      167
Homogeneity (Cartan — Siegel) domain of type II      169
Homogeneity (Cartan — Siegel) domain of type III      171
Homogeneity (Cartan — Siegel) domain of type IV      172
Homogeneous space      100
Homotopic paths      78
Ideal generated by forms      221
Ideal of Lie algebra      95
Index, Maslov      160
Index, Morse      158
Index, Morse — Maslov — Arnold, in the form of Leray — Kashivara      159
Index, of a functional      35
Invariant integral      54
Isometry      100
Isometry, local      100
Jacobi condition      30
Legendre condition      26
Legendre — Caratheodory condition      252
Legendre — Weyl condition      242
Lie algebra      84
Lie algebra, abelian      96
Lie algebra, center of      96
Lie algebra, compact      98
Lie algebra, orthogonal, with involution      106 122
Lie algebra, semisimple      96
Lie algebra, simple      96
Lift of a manifold      54
Linear connection coefficients      229
Manifold, Grassmann      69 112
Manifold, Grassmann, complex      72
Manifold, Kahler      184
Manifold, Lagrange — Grassmann      119 156
Manifold, Legendre      50
Manifold, lift of a      54
Manifold, locally symmetrical at a point      102
Manifold, pseudo-Riemannian      99
Manifold, Riemannian      9
Manifold, simply connected      78
Manifold, stratified      177
Manifold, symmetrical      102
Manifold, topological      69
Matrix double ratio      131
Matrix Riccati equation      31 61
Maximal set of isoclinic planes      141
Minimum, strong      43
Minimum, weak      6
Monodromy matrix      198
Multiplicity of a point      35
Pair, symmetrical Riemann      105
Pairs of points, equidistant      138
Pairs of points, equivalent      139
Parallel translation      228
Plane, horizontal      69 112
Plane, isoclinic      132
Plane, isotropic      149
Plane, Lagrangian      117 156
Plane, semiorthogonal      154
Plane, stabilizer of      114
Plane, vertical      69 112
Planes Clifford parallel      153 155
Plucker embedding      116
Problem, associated extremal      28 215
Problem, brachistrochrone      5
Problem, Lagrange      63
Problem, linear-quadratic      64
Problem, Plataeu      208
Projection, natural      100
Quadruple of planes, biharmonic      148
Quadruple of planes, harmonic      131
Quaternion      73
Riccati equation      2
Riccati partial differential equation      260
Schwartz equation      203
Schwartz operator (derivative)      200
Schwartz operator, matrix      205
Second variation of a functional      25 215
Section of a bundle      219
Sets of congruent planes      142
Signature of a quadratic form      159
Skew-inner product      118
Space, bundle      217
Space, elliptic      151 154
Space, globally symmetrical      102
Space, isotropic      117
Space, symmetrical      102
Space, symmetrical, Hermitian      167
Stabilizer of a plane      114
Stratum      178
Strengthened Jacobi condition      30
Strengthened Legendre condition      27
Subalgebra of a Lie algebra      94
Subgroup, invariant (normal)      95
Subgroup, isotropy      100
Subgroup, of a Lie group      94
Subgroup, one-parameter      104
Subgroup, stationary      100
Submanifold, geodesic at a point      107
Submanifold, integral      50 224
Submanifold, totally geodesic      107
Subspace, horizontal      227
Subspace, vertical      227
Symplectic structure      83
Torsion of connection      233
Transformation, Caratheodory      244
Transformation, Cayley      185
Transformation, contact      244
Transformation, generalized linear-fractional      70 113
Transformation, Legendre — Weyl      240
Transformation, monodromy      198
Transvection      102
Transversality conditions      19
Triple Lie system      108
Variation equation      216
Variation geodesic      217
Vector, tangent      85
Vectors, skew-orthogonal      118
Weierstrass function      44
Weierstrass — Erdman condition      22
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте