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" The Geometry of Higher-Order Hamilton Spaces : "
by Radu Miron.
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BL
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| Record Number
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774197
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b594191
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| Main Entry
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by Radu Miron.
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The Geometry of Higher-Order Hamilton Spaces : : Applications to Hamiltonian Mechanics\ by Radu Miron.
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| Publication Statement
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Dordrecht : Springer Netherlands, 2003
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| Series Statement
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Fundamental Theories of Physics, An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application, 132
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| ISBN
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9401000700
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: 940103995X
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: 9789401000703
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: 9789401039956
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| Contents
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1 Geometry of the k-Tangent Bundle TkM.- 1.1 The Category of k-Accelerations Bundles.- 1.2 Liouville Vector Fields. k-Semisprays.- 1.3 Nonlinear Connections.- 1.4 The Dual Coefficients of a Nonlinear Connection.- 1.5 The Determination of a Nonlinear Connection.- 1.6 d-Tensor Fields. N-Linear Connections.- 1.7 Torsion and Curvature.- 2 Lagrange Spaces of Higher Order.- 2.1 Lagrangians of Order k.- 2.2 Variational Problem.- 2.3 Higher Order Energies.- 2.4 Jacobi-Ostrogradski Momenta.- 2.5 Higher Order Lagrange Spaces.- 2.6 Canonical Metrical N-Connections.- 2.7 Generalized Lagrange Spaces of Order k.- 3 Finsler Spaces of Order k.- 3.1 Spaces F(k)n.- 3.2 Cartan Nonlinear Connection in F(k)n.- 3.3 The Cartan Metrical N-Linear Connection.- 4 The Geometry of the Dual of k-Tangent Bundle.- 4.1 The Dual Bundle (T*k M, ?*k, M).- 4.2 Vertical Distributions. Liouville Vector Fields.- 4.3 The Structures J and J*.- 4.4 Canonical Poisson Structures on T*kM.- 4.5 Homogeneity.- 5 The Variational Problem for the Hamiltonians of Order k.- 5.1 The Hamilton-Jacobi Equations.- 5.2 Zermelo Conditions.- 5.3 Higher Order Energies. Conservation of Energy ?k ?1(H).- 5.4 The Jacobi-Ostrogradski Momenta.- 5.5 Nother Type Theorems.- 6 Dual Semispray. Nonlinear Connections.- 6.1 Dual Semispray.- 6.2 Nonlinear Connections.- 6.3 The Dual Coefficients of the Nonlinear Connection N.- 6.4 The Determination of the Nonlinear Connection by a Dual k-Semispray.- 6.5 Lie Brackets. Exterior Differential.- 6.6 The Almost Product Structure ?. The Almost Contact Structure
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| LC Classification
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QA689.B973 2003
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| Added Entry
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Radu Miron
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