52 citations · 65 across the 9 of their papers we have counts for
5 papers · 1 filter
Geometric structure-preserving optimal control of the rigid body
Anthony M. Bloch, Islam I. Hussein, Melvin Leok +1
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an ini…
Dynamics of Symplectic SubVolumes
Jared M. Maruskin, Daniel J. Scheeres, Anthony M. Bloch
In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct applicati…
The Boltzmann-Hamel Equations for Optimal Control
Jared M. Maruskin, Anthony M. Bloch
We extend the Boltzmann-Hamel equations to the optimal control setting, producing a set of equations for both kinematic and dynamic nonholonomic optimal control problems. In partic…
Hill's Equation with Random Forcing Terms
Fred Adams, Anthony Bloch
Motivated by a class of orbit problems in astrophysics, this paper considers solutions to Hill's equation with forcing strength parameters that vary from cycle to cycle. The result…
Controlled Lagrangians and Stabilization of Discrete Mechanical Systems I
Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden +1
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as brok…