202 research outputs found
Dirac Optimal Reduction
The purpose of this paper is to generalize the (Poisson) Optimal Reduction Theorem in Ortega and Ratiu [Momentum Maps and Hamiltonian Reduction. Progress in Mathematics 222. Boston, MA: Birkhäuser. xxxiv, 497pp., 2004] to general proper Lie group actions on Dirac manifolds, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reductio
Asymptotic Stability, Instability and Stabilization of Relative Equilibria
In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev
Discrete rigid body dynamics and optimal control
We analyze an alternative formulation of the rigid body equations, their relationship with the discrete rigid body equations of Moser-Veselov (1991) and their formulation as an optimal control problem. In addition we discuss a general class of discrete optimal control problems
On a unified formulation of completely integrable systems
The purpose of this article is to show that a differential
system on which admits a set of independent
conservation laws defined on an open subset , is
essentially equivalent on an open and dense subset of ,
with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \
u^\prime_n=u_n$. The main results are illustrated in the case of two concrete
dynamical systems, namely the three dimensional Lotka-Volterra system, and
respectively the Euler equations from the free rigid body dynamics.Comment: 11 page
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