14 citations · 35 across the 19 of their papers we have counts for
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On the Geometry of Multi-Dirac Structures and Gerstenhaber Algebras
Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok
In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the…
Stokes-Dirac Structures through Reduction of Infinite-Dimensional Dirac Structures
Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok +1
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how St…
A Discrete Theory of Connections on Principal Bundles
Melvin Leok, Jerrold E. Marsden, Alan D. Weinstein
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of co…