73 citations · 945 across the 70 of their papers we have counts for
80 papers
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…
Symmetric Toda, gradient flows, and tridiagonalization
Anthony M. Bloch, Steven N. Karp
The Toda lattice (1967) is a Hamiltonian system given by points on a line governed by an exponential potential. Flaschka (1974) showed that the Toda lattice is integrable by in…
Virtual Affine Nonholonomic Constraints
Efstratios Stratoglou, Alexandre Anahory Simoes, Anthony Bloch +1
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems ar…
Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage
Alexandre Anahory Simoes, Asier López-Gordón, Anthony Bloch +1
Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical sim…
Virtual Nonholonomic Constraints: A Geometric Approach
Alexandre Anahory Simoes, Efstratios Stratoglou, Anthony Bloch +1
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanic…
On two notions of total positivity for partial flag varieties
Anthony M. Bloch, Steven N. Karp
Given integers , let denote the type partial flag variety consisting of all chains of subspaces $(V_{k_1}\subset…