106 citations · 677 across the 72 of their papers we have counts for
6 papers · 1 filter
Generating Functionals and Lagrangian PDEs
Joris Vankerschaver, Cuicui Liao, Melvin Leok
We introduce the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Ja…
Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints
Melvin Leok, Tomoki Ohsawa, Diana Sosa
We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians a…
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…
Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3)
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in in…
General Techniques for Constructing Variational Integrators
Melvin Leok, Tatiana Shingel
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximat…
Prolongation-Collocation Variational Integrators
Melvin Leok, Tatiana Shingel
We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smoot…