Non-holonomic equations for the normal extremals in geometric control theory

Hamilton equations for non-holonomic systems

Hamilton equations for Lagrangian systems on fibred manifolds, subjected to general non-holonomic constraints (i.e., not necessarily affine in the velocities) are studied. Conditions for existence of a non-holonomic Legendre transformation are discussed, and the corresponding formulas for constraint momenta and Hamiltonian are found.

Non-Holonomic Attitude Control

Non-holonomic Control I

In this paper, we present a universal control technique, the non-holonomic control, which allows us to impose any arbitrarily prescribed unitary evolution to any quantum system through the alternate application of two well-chosen perturbations.

Non-holonomic Control Ii : Non-holonomic Quantum Devices

In this paper, we show how the non-holonomic control technique can be employed to build completely controlled quantum devices. Examples of such controlled structures are provided.

The Algebra of Holonomic Equations

In this article algorithmic methods are presented that have essentially been introduced into computer algebra systems like Maple or Mathematica within the last decade. The main ideas are due to Stanley and Zeilberger. Some of them had already been discovered in the last century by Beke, but because of their complexity the underlying algorithms have fallen into oblivion. We give a survey of thes...