Routh Reduction by Stages
نویسندگان
چکیده
منابع مشابه
Routh Reduction by Stages
This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems ...
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This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge–Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical fea...
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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...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2011
ISSN: 1815-0659
DOI: 10.3842/sigma.2011.109