**Acronym:** ROBOTTOPES

**Scientist in charge:** Manuel de León

**Experienced Researcher:** Amna Shaddad

**Project Reference:** 846722

**Start Date:** 2020-09-16

**End Date:** 2022-09-15

**Abstract:**

The plan of the project is to extend momentum polytope theory for the standard momentum mapping to the case of nonholonomic momentum mapping. Nonholonomic constraints often arise in rolling systems, such as a ball that rolls without slipping on a table. Problems of nonholonomic mechanics therefore include those in robotics, wheeled vehicular dynamics and motion generation which are one of the forefronts of scientific research now. In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. Continuous symmetries can be described by Lie groups. Geometric Mechanics is the mechanics on Lie groups and the manifolds on which they act. It is effectively a means for describing any mechanical system including the mechanics of particles and rigid bodies; continuum mechanics; field theory; quantum mechanics. A momentum map of the system extends the notions of linear and angular momentum in classical mechanics to arbitrary Hamiltonian systems.

Describing the image of a momentum map defined on a symplectic manifold has generated a large amount of research and remains, to this day, one of the most active areas in symplectic geometry and its applications to Hamiltonian dynamics, especially bifurcation theory. The intersection of the momentum map action on a manifold with the positive Weyl chamber is convex and called the momentum polytope which plays the role of an a priori bifurcation diagram for any symmetric Hamiltonian system. Recent results have extended momentum polytope theory so that they can now give information about the configurations, relative equilibria and reduced spaces of a mechanical system.

*This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 846722.*