All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 94

Showing per page

The existence of limit cycle for perturbed bilinear systems

Hanen Damak, Mohamed Ali Hammami, Yeong-Jeu Sun (2012)

Kybernetika

In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter ε to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...

The geometry of Calogero-Moser systems

Jacques Hurtubise, Thomas Nevins (2005)

Annales de l’institut Fourier

We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the r -th power of the elliptic curve, where r is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...

The geometry of Newton's law and rigid systems

Marco Modugno, Raffaele Vitolo (2007)

Archivum Mathematicum

We start by formulating geometrically the Newton’s law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. For constrained systems we have intrinsic and extrinsic viewpoints, with respect to the environmental space. Multi–particle systems are modelled on n -th products of the pattern model. We apply the above scheme to discrete rigid systems. We study the splitting of the tangent and cotangent environmental space into the three components of center...

The geometry of nondegeneracy conditions in completely integrable systems (corrected version of fascicule 4, volume XIV, 2005, p. 705-719)

Nicolas Roy (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using the notion of regular completely integrable systems defined by a fibration of a symplectic manifold by lagrangian tori together with a Hamiltonian function constant on the fibers. In this paper, we give a geometrical definition of different nondegeneracy conditions,...

The inverse problem in the calculus of variations: new developments

Thoan Do, Geoff Prince (2021)

Communications in Mathematics

We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of n second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas’s famous solution for n = 2 . We then examine a new class of solutions in arbitrary dimension n and give some non-trivial examples in dimension 3.

The Lagrange rigid body motion

Tudor Ratiu, P. van Moerbeke (1982)

Annales de l'institut Fourier

We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of s o ( 3 ) × s o ( 3 ) ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group S O ( 3 ) × s o ( 3 ) with its natural...

The Lagrangian and Hamiltonian formulations for the waves in a compressible fluid with the Hall current.

Giulio Mattei (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si ricavano: 1) l'equazione d'onda linearizzata, 2) la formulazione Lagrangiana, 3) la formulazione Hamiltoniana, nella teoria della propagazione ondosa in un fluido comprimibile descritto dalle equazioni della magnetofluidodinamica ideale in presenza di corrente Hall.

Currently displaying 21 – 40 of 94