An affine framework for analytical mechanics
Pawel Urbanski
TL;DR
This paper develops an affine Cartan calculus framework, introducing special affine bundles and duality, and establishes canonical isomorphisms crucial for Lagrangian and Hamiltonian dynamics in affine geometry.
Contribution
It introduces a novel affine Cartan calculus with special affine bundles and duality, providing foundational isomorphisms for affine mechanics formulations.
Findings
Established affine Cartan calculus framework.
Introduced special affine bundles and duality concepts.
Proved canonical isomorphisms for affine Lagrangian and Hamiltonian dynamics.
Abstract
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Black Holes and Theoretical Physics