de Leon M., Rodrigues P.R. — Methods of differential geometry in analytical mechanics :: Электронная библиотека попечительского совета мехмата МГУ

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de Leon M., Rodrigues P.R. — Methods of differential geometry in analytical mechanics

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Название: Methods of differential geometry in analytical mechanics

Авторы: de Leon M., Rodrigues P.R.

Аннотация:

The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint. Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories. The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 495

Добавлена в каталог: 17.11.2013

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Предметный указатель

Symmetric, product      39
Symmetrizing mapping      38
Symplectic, automorphism      229
Symplectic, basis      229
Symplectic, canonical symplectic form on       239
Symplectic, coordinate neighborhood      251
Symplectic, coordinates      251
Symplectic, diffeomorphism      236
Symplectic, form on a vector space      229
Symplectic, form on manifolds      236
Symplectic, frame      234
Symplectic, group      229
Symplectic, infinitesimal symplectic transformation      237
Symplectic, isomorphism      229
Symplectic, linear mapping      229
Symplectic, manifold      236
Symplectic, structure on a vector space      229
Symplectic, structure on manifolds      236
Symplectic, submanifold      236
Symplectic, subspace      231
Symplectic, transformation      236
Symplectic, vector bundle      232
Symplectic, vector field      237
Symplectic, vector space      229
Symplectic, vector subbundle      232
Symplectomorphism      104 236
Tangent, bundle      23 27
Tangent, bundle of order       452
Tangent, covector      28
Tangent, curves at a point      15
Tangent, curves at the order       451
Tangent, space      16
Tangent, vector, of a curve      15
Target projection      452
Tension of a connection      202
Tensor, algebra      35
Tensor, field of type on a manifold      36
Tensor, of type       34
Tensor, product      31
Tensor, skew-symmetric tensor      36
Tensor, space of type       34
Tensor, symmetric tensor      36
Topological, invariant      72
Topological, manifold      5
Torsion, strong torsion      211
Torsion, tensor      78 213
Torsion, weak torsion      211
Total force      439
Transformation of a manifold      8

Tulczyjew differential operator      455
Unitary, frame      162
Unitary, group      86
Universal factorization property      31
Variation      350
Variation vector field      380
Variational problem      350
Vector bundle      23
Vector bundle, -vector bundle homomorphism      23
Vector bundle, -vector bundle isomorphism      23
Vector bundle, homomorphism      23
Vector bundle, induced vector bundle      24
Vector bundle, isomorphism      23
Vector bundle, local triviality for a vector bundle      23
Vector bundle, quotient vector bundle      25
Vector bundle, real vector bundle      23
Vector bundle, restricting a vector bundle      24
Vector bundle, transition functions of a vector bundle      110
Vector bundle, trivial vector bundle      24
Vector field      17
Vector field, fundamental vector field      95
Vector field, time-dependent vector field      249
Vector fields related by a mapping      106 298 371
Vector form      190
Vector subbundle      25
Vertical, bundle of       114
Vertical, bundle of       240
Vertical, component of a vector field      197
Vertical, derivation on       183
Vertical, differentiation on       184
Vertical, distribution      197
Vertical, projector      197 339
Vertical, subspace to       197
Vertical, tangent vector to       114
Vertical, tangent vector to       240
Vertical, vector field on       114
Vertical, vector field on       241
Volume form, natural volume form      63
Volume form, on a manifold      62
Volume form, on a vector space      61
Weak horizontal, bundle      338
Weak horizontal, lift      338
Weak horizontal, projector      339
Weak horizontal, subspace      338
Weak horizontal, vector field      338
Weak, -torsion      341
Weak, $\bar{J}$ -torsion      341
Weak, curvature      341
Whitney sum of vector bundles      25

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