REVIEW 1 cited by
Lagrangian Reduction, the Euler--Poincar\'{e} Equations, and Semidirect Products
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. These reduced variational principles are interesting in their own right since they involve constraints on the allowed variations, analogous to what one finds in the theory of nonholonomic systems with the Lagrange d'Alembert principle. In addition, the abstract theorems about circulation, what we call the Kelvin-Noether theorem, are given.
Forward citations
Cited by 1 Pith paper
-
Distributed Pose Graph Optimization via Continuous Riemannian Dynamics
Pose graph optimization is recast as damped Riemannian dynamics on Lie groups, enabling a fully distributed algorithm with a semi-implicit integrator that converges under both synchronous and asynchronous communication.
Discussion (0). Sign in to comment.