73 citations · 945 across the 70 of their papers we have counts for
4 papers · 1 filter
A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices
Anthony M. Bloch, Arieh Iserles, Jerrold E. Marsden +1
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fome…
Optimal Control of Underactuated Nonholonomic Mechanical Systems
Islam I. Hussein, Anthony M. Bloch
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at m…
A Discrete Variational Integrator for Optimal Control Problems on SO(3)
Islam I. Hussein, Melvin Leok, Amit K. Sanyal +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…
Orbits in Extended Mass Distributions: General Results and the Spirographic Approximation
Fred C. Adams, Anthony M. Bloch
This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potent…