19 citations · 23 across the 21 of their papers we have counts for
23 papers
Variational Dissipative Mechanics on Lie Algebroids
Alexandre Anahory Simoes, Leonardo Colombo
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional s…
Mechanical Hamiltonization of unreduced -simple Chaplygin systems
Alexandre Anahory Simoes, Juan Carlos Marrero, David Martín de Diego
In this paper, we prove that the trajectories of unreduced -simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian…
Symmetry reduction and reconstruction in contact geometry and Lagrange-Poincaré-Herglotz equations
Alexandre Anahory Simoes, Leonardo Colombo, Manuel de Leon +2
In this paper, we investigate the reduction process of a contact Lagrangian system whose Lagrangian is invariant under a group of symmetries. We give explicit coordinate expression…
Comparison of two numerical methods for Riemannian cubic polynomials on Stiefel manifolds
Alexandre Anahory Simoes, Leonardo Colombo, Fátima Silva Leite
In this paper we compare two numerical methods to integrate Riemannian cubic polynomials on the Stiefel manifold . The first one is the adjusted de Casteljau alg…
Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance
Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo
It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational o…
On the Geometry of Virtual Nonlinear Nonholonomic Constraints
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch +1
Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic syst…