Tulczyjew triples in higher derivative field theory
From MaRDI portal
Publication:888750
DOI10.3934/jgm.2015.7.1zbMath1367.70062arXiv1406.6503OpenAlexW3124896854MaRDI QIDQ888750
Katarzyna Grabowska, Luca Vitagliano
Publication date: 2 November 2015
Published in: Journal of Geometric Mechanics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1406.6503
variational calculusHamiltonian formalismLagrangian formalismjet spacesclassical field theoryTulczyjew triple
Symplectic manifolds (general theory) (53D05) Hamilton's equations (70H05) Jets in global analysis (58A20) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Lagrange's equations (70H03)
Related Items
Second-order constrained variational problems on Lie algebroids: applications to optimal control ⋮ Covariant Hamiltonian field theories on manifolds with boundary: Yang-Mills theories ⋮ Symplectic structures related with higher order variational problems ⋮ A new multisymplectic unified formalism for second order classical field theories ⋮ The dressing field method in gauge theories -- geometric approach ⋮ Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction ⋮ On the geometry of the Schmidt-Legendre transformation ⋮ De Donder Construction for Higher Jets ⋮ The Tulczyjew triple in mechanics on a Lie group ⋮ Linear duals of graded bundles and higher analogues of (Lie) algebroids ⋮ Models for higher algebroids ⋮ Regularity properties of fiber derivatives associated with higher-order mechanical systems ⋮ Geometry of Routh reduction ⋮ A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- AV-differential geometry: Poisson and Jacobi structures
- Lagrangian and Hamiltonian formalism in field theory: a simple model
- Hamiltonian structures and generating families
- A symplectic framework of linear field theories
- The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. I: The linear theory
- The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. II: The nonlinear theory
- Double affine bundles
- The Lagrangian-Hamiltonian formalism for higher-order field theories
- AV-differential geometry: Euler-Lagrange equations
- AV-differential geometry and Newtonian mechanics
- A Tulczyjew triple for classical fields
- GEOMETRIC HAMILTON–JACOBI FIELD THEORY
- Liouville structures
- THE HAMILTON–JACOBI FORMALISM FOR HIGHER-ORDER FIELD THEORIES
- Unambiguous formalism for higher order Lagrangian field theories
- Symplectic structures related with higher order variational problems
- Double vector bundles and duality
- Geometric Hamilton–Jacobi theory for higher-order autonomous systems