Geometric Mechanics at UNS
"Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics." --- Leonardo da Vinci
Research areas
The interest in the geometrical focus in mechanics has grown in the last decades. The framework provided by differential geometry gives us useful tools for the study of systems in mechanics and field theory, where concepts such as symplectic manifolds, jet bundles, groups and groupoids becomes essential. Conversely, mathematical physics remains as a source of constructions and theoretical results. Our research is guided by these facts.
More specifically, this group works in developing knowledge in basic sciences regarding geometric mechanics, both from the theoretical point of view as well as from the applications to relevant physical and mathematical problems, mainly in two branches: theory reduction by symmetry in the symplectic case and in the Lagrangian case in field theory. Also discrete formalism is been studied by developing geometric integrators, that is, numerical methods that respect geometric structures. In both the discrete and continuous fields, the group studies different cases of systems reduced by a symmetry group.
A new line of research for the group studies the use of neural networks to deal with mechanical systems with holonomic and nonholonomic constraints, and with different examples of interest in mechanics.
Topics of interest
Reduction theory in mechanics and classical field theory
Cotangent bundle reduction by stages.
Lagrangian reduction in field theory.
Routh reduction in polysymplectic formalism.
Development of variational integrators
Formulation of geometric integrators for Griffiths' variational problems.
Parallelization of geometric integrators for optimal control.
Applications to examples
of interest
Euler's disk.
Coupled rigid bodies.
Rigid body with rotors.
People
Santiago Capriotti , associate professor at Universidad Nacional del Sur (UNS), researcher at Instituto de Matemática de Bahía Blanca (INMABB) and assistant researcher at Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
Hernán Cendra , emeritus professor at Universidad Nacional del Sur.
Viviana Díaz , assistant professor at Universidad Nacional del Sur (UNS) and researcher at Instituto de Matemática de Bahía Blanca (INMABB).
Sebastián Ferraro , full professor at Universidad Nacional del Sur (UNS), researcher at Instituto de Matemática de Bahía Blanca (INMABB) and adjunct researcher at Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
Eduardo García-Toraño Andrés , teaching assistant at Universidad Nacional del Sur (UNS).
Guadalupe Quijón , teaching assistant at Universidad Nacional del Sur (UNS) and predoctoral fellow at Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
Presentation of research lines
(In Spanish)
