Lagrangian and Hamiltonian geometries. Applications to Analytical Mechanics

Description

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