دانلود کتاب Lagrangian and Hamiltonian geometries. Applications to Analytical Mechanics

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Preface......Page 7
I Lagrange and Hamilton Spaces......Page 15
Riemannian mechanical systems......Page 19
The evolution semispray of the mechanical system TEXT......Page 22
The nonlinear connection of TEXT......Page 28
The canonical metrical connection TEXT......Page 34
Semidefinite Finsler spaces......Page 39
The notion of Finslerian mechanical system......Page 41
The evolution semispray of the system TEXT......Page 44
The canonical nonlinear connection of the Finslerian mechanical systems TEXT......Page 46
The dynamical derivative determined by the evolution nonlinear connection TEXT......Page 48
Metric N-linear connection of TEXT......Page 52
The electromagnetism in the theory of the Finslerian mechanical systems TEXT......Page 55
The almost Hermitian model on the tangent manifold TEXT of the Finslerian mechanical systems TEXT......Page 57
Lagrange Spaces. Preliminaries......Page 61
Lagrangian Mechanical systems, TEXT......Page 65
The evolution semispray of TEXT......Page 67
The evolution nonlinear connection of TEXT......Page 68
Hamilton spaces. Preliminaries......Page 71
The Hamiltonian mechanical systems......Page 75
Canonical nonlinear connection of TEXT......Page 79
The Cartan mechanical systems......Page 83
Parallelism, paths and structure equations......Page 89
Lagrangian Mechanical systems of order TEXT......Page 95
Lagrangian mechanical system of order TEXT, TEXT......Page 98
Canonical TEXTsemispray of mechanical system TEXT......Page 99
Canonical nonlinear connection of mechanical system TEXT......Page 101
Canonical metrical TEXTconnection......Page 102
Notion of Cartan space......Page 105
Canonical nonlinear connection of TEXT......Page 108
Canonical metrical connection of TEXT......Page 110
The duality between Lagrange and Hamilton spaces......Page 112
II Lagrangian and Hamiltonian Spaces of higher order......Page 117
The electromagnetism in the theory of the Riemannian mechanical systems TEXT......Page 138
The almost Hermitian model of the RMS TEXT......Page 140
III Analytical Mechanics of Lagrangian and Hamiltonian Mechanical Systems......Page 163
Canonical TEXTmetrical connection of TEXT. Structure equations......Page 215
The almost Hermitian model of the Lagrangian mechanical system TEXT......Page 218
Generalized Lagrangian mechanical systems......Page 220
The Riemannian TEXT almost contact model of the Lagrangian mechanical system of order TEXT, TEXT......Page 249
Classical Riemannian mechanical system with external forces depending on higher order accelerations......Page 251
Finslerian mechanical systems of order TEXT, TEXT......Page 254
Hamiltonian mechanical systems of order TEXT......Page 257