34 citations · 50 across the 12 of their papers we have counts for
15 papers
Optimal Synthesis on the Special Linear Group
Marcus T. C. Lau, Alejandro Bravo-Doddoli
We study the exponential map on the group of real two-by-two matrices with determinant one, endowed with a left-invariant Riemannian metric. Using the Euler-Poincaré equation and i…
The Integrability of a knife-edge Billiard in a Disk
Alejandro Bravo-Doddoli, Huaidian Hou, William Clark +1
This paper proves the integrability of a nonholonomic billiard defined by a knife-edge in a disk. The paper begins by parametrizing the impact space using coordinates that reveal t…
Metric Lines in the Space of Curves
Daniella Catalá, Miriam Vollmayr-Lee, Alejandro Bravo-Doddoli
This paper investigates sub-Riemannian geodesics in the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing geode…
Abelian instances of nonabelian symplectic reduction
A. Bravo-Doddoli, L. C. García-Naranjo, E. Rigato
Let be a Lie group with a normal abelian subgroup , and let be a symplectic manifold endowed with a Hamiltonian -action. We investigate…
Integrable sub-Riemannian geodesic flows on the special orthogonal group
Alejandro Bravo-Doddoli, Philip Arathoon, Anthony M. Bloch
We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metri…
Metric Lines in the Special Euclidean group on the plane
Y. Wang, S. Ku, A. Bravo-Doddoli
The Special Euclidean group on the plane has the left-invariant sub-Riemannian structure. Every sub-Riemannian manifold possesses a Hamiltonian function governing the sub-R…
Metric Lines in Engel-type Groups
Alejandro Bravo-Doddoli
In the framework of sub-Riemannian manifolds, a natural question is: What are the ''metric lines'' (i.e., isometric embeddings of the real line)? This article presents a conjecture…
Sympletic reduction of the sub-Riemannian geodesic flow for metabelian nilpotent groups
Alejandro Bravo-Doddoli, Enrico Le Donne, Nicola Paddeu
We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundl…
Chaotic subRiemannian geodesic flow in
Alejandro Bravo-Doddoli
The space of -jets of a real function of two real variables, denoted by , admits the structure of a metabelian Carnot group, so $J^2(\mathbb{R}^2,\…
No Periodic normal Geodesics in
Alejandro Bravo-Doddoli
The space of -jets of real function of one real variable admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamilt…
Metric lines in Jet Space
Alejandro Bravo-Doddoli
Given a sub-Riemannian manifold, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of -jets of a real function of one real vari…
No Periodic Geodesics in Jet Space
Alejandro Bravo-Doddoli
The space of -jets of a real function of one real variable admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, a…
Geodesics in Jet Space
Alejandro Bravo-Doddoli, Richard Montgomery
The space of -jets of a real function of one real variable admits the structure of Carnot group type. As such, admits a submetry (\sR submersion) onto the Euclid…
Higher Elastica: Geodesics in the Jet Space
Alejandro Bravo-Doddoli
Carnot groups are subRiemannian manifolds. As such they admit geodesic flows, which are left-invariant Hamiltonian flows on their cotangent bundles. Some of these flows are integra…
The dynamics of an articulated -trailer vehicle
Alejandro Bravo-Doddoli, Luis C. García-Naranjo
We derive the reduced equations of motion for an articulated -trailer vehicle that moves under its own inertia on the plane. We show that the energy level surfaces in the reduce…