Lagrangian reduction by stages for non-holonomic systems in a Lie algebroid framework

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lagrangian reduction by stages for non-holonomic systems in a Lie algebroid framework

The Lagrange-d’Alembert equations of a non-holonomic system with symmetry can be reduced to the Lagrange-d’Alembert-Poincaré equations. In a previous contribution we have shown that both sets of equations fall in the category of so-called ‘Lagrangian systems on a subbundle of a Lie algebroid’. In this paper, we investigate the special case when the reduced system is again invariant under a new ...

متن کامل

A Lie algebroid framework for non-holonomic systems

In order to obtain a framework in which both non-holonomic mechanical systems and non-holonomic mechanical systems with symmetry can be described, we introduce in this paper the notion of a Lagrangian system on a subbundle of a Lie algebroid.

متن کامل

Lie algebroid structures and Lagrangian systems on affine bundles

As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.

متن کامل

Lagrangian Reduction by Stages

Setting. Let (X, g) be a given Riemannian manifold and let ∇ be the corresponding LeviCivita connection. Let G be a compact Lie group with a bi-invariant Riemannian metric κ. Let π : Q → X be a principal bundle with structure group G acting on the left, let A be a principal connection on Q, and let B be the curvature of A. 46 4. Wong’s Equations and Coordinate Formulas Now define the Lagrangian...

متن کامل

The Lie Algebra of a Lie Algebroid

We present results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps. We also prove that every isomorphism of such Lie algebras induces diffeomorphism of base manifolds respecting the generalized foliations defined by the anchor maps.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Physics A: Mathematical and General

سال: 2005

ISSN: 0305-4470,1361-6447

DOI: 10.1088/0305-4470/38/47/008