70 citations · 388 across the 29 of their papers we have counts for
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math.SG2023★ 1 cited
Hamiltonian mechanics and Lie algebroid connections
Jiawei Hu, Ari Stern
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivializa…
math.SG2011★ 11 cited
Symplectic groupoids and discrete constrained Lagrangian mechanics
Juan Carlos Marrero, David Martín de Diego, Ari Stern
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of s…
math.SG2009★ 10 cited
Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids
Ari Stern
We present a discrete analog of the recently introduced Hamilton-Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to disc…