Hamiltonian treatment of non-conservative systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911075615637504 |
|---|---|
| author | Aykroyd, Christopher Bourgoin, Adrien Poncin-Lafitte, Christophe Le |
| author_facet | Aykroyd, Christopher Bourgoin, Adrien Poncin-Lafitte, Christophe Le |
| contents | We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties regarding boundary conditions, the emergence of the physical-limit trajectory, and the decomposition of the Lagrangian into conservative and dissipative sectors. Importantly, we demonstrate that the redundant doubled configuration space admits a gauge freedom at the level of the canonical momenta that leaves the physical dynamics unchanged. From a Legendre transform, we construct the corresponding family of gauge-related nonconservative Hamiltonians; we show that virtually any classical initial-value problem can be embedded on our enlarged symplectic manifold, supplying the associated Hamiltonian and Lagrangian functions explicitly. As a further contribution, we derive a completely equivalent linear ``Lie'' formulation of the double-variable action and Hamiltonian which streamlines computations and renders transparent many structural properties of the formalism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian treatment of non-conservative systems Aykroyd, Christopher Bourgoin, Adrien Poncin-Lafitte, Christophe Le Classical Physics Mathematical Physics We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley's initial-value action, we clarify important subtleties regarding boundary conditions, the emergence of the physical-limit trajectory, and the decomposition of the Lagrangian into conservative and dissipative sectors. Importantly, we demonstrate that the redundant doubled configuration space admits a gauge freedom at the level of the canonical momenta that leaves the physical dynamics unchanged. From a Legendre transform, we construct the corresponding family of gauge-related nonconservative Hamiltonians; we show that virtually any classical initial-value problem can be embedded on our enlarged symplectic manifold, supplying the associated Hamiltonian and Lagrangian functions explicitly. As a further contribution, we derive a completely equivalent linear ``Lie'' formulation of the double-variable action and Hamiltonian which streamlines computations and renders transparent many structural properties of the formalism. |
| title | Hamiltonian treatment of non-conservative systems |
| topic | Classical Physics Mathematical Physics |
| url | https://arxiv.org/abs/2507.18658 |