106 citations · 677 across the 72 of their papers we have counts for
4 papers · 1 filter
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…
Discrete Exterior Calculus
Mathieu Desbrun, Anil N. Hirani, Melvin Leok +1
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Ou…
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…