Project description
Extending the theoretical descriptions of momentum polytopes to practical applications
A polytope is the convex hull of finitely many points in a Euclidean space. A polytope is a generalisation in any number of dimensions of the three-dimensional polyhedron or two-dimensional polygon. The German term polytop was coined by the mathematician Reinhold Hoppe, and was introduced to English mathematicians as polytope by Alicia Boole Stott, the daughter of Georges Boole. Polytopes are more than abstract mathematical concepts. In fact, they are very useful tools in real life with applications in many areas of mathematics and computer graphics. Despite that, the study of the special case of momentum polytopes related to momentum mapping has largely focussed on theoretical aspects rather than practical applications. The EU-funded ROBOTTOPES project is extending momentum polytope theory to important applications in quantum mechanics and robotic systems.
Objective
The plan of the project is to extend momentum polytope theory for the standard momentum mapping three different scenarios: (1) the case of contact hamiltonian systems; (2) the mathematical description of nonholonomic (robotic) systems and (3) multisymplectic field theories. The state of the art of research on momentum polytopes has been primarily focussed on the theoretical aspects rather than interdisciplinary research and applications, so this work will open up new grounds of research. The study of general multisymplectic manifolds is not only crucial to understand dynamics but is also of great independent interest e.g. for the quantisation of mechanics or field theories.
Fields of science
Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
28006 Madrid
Spain