5 papers · 1 filter
Dirac Structures and Reduction of Optimal Control Problems with Symmetries
A. Ibort, M. Leok, R. Salmoni +1
We study the symmetry reduction of optimal control problems using Dirac structures. The first-order conditions of the Pontryagin Maximum Principle are written as an implicit Dirac…
A Morse-Family Integrator for Hamilton--Jacobi Dynamics Across Caustics
F. Jiménez Alburquerque, M. Leok, C. Sardón +1
We develop a geometric framework for implicit discrete Hamiltonian systems based on discrete Morse families, Lagrangian relations, and discrete analogues of Tulczyjew's triple. The…
Noether-Type Theorems and the Generalized Herglotz Principle in -Contact Geometry
Melvin Leok, Cristina Sardón, Xuefeng Zhao
We develop a unified geometric framework for dissipative mechanical systems based on uniform -contact manifolds, which provide an extended phase space equipped with multiple con…
Integration on -Cosymplectic Manifolds
M. Leok, C. Sardón, X. Zhao
This paper presents a unified framework for studying dynamics and integration on -cosymplectic manifolds. After outlining the geometric foundations of -cosymplectic structure…
q-Cosymplectic Geometry, Integrability and Reduction
Melvin Leok, Cristina Sardón, Xuefeng Zhao
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Se…