Discrete Routh reduction
نویسندگان
چکیده
منابع مشابه
Discrete Routh reduction
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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This chapter investigates the relationship between Routh symmetry reduction and time discretization for Lagrangian systems. Within the framework of discrete variational mechanics, a discrete Routh reduction theory is constructed for the case of abelian group actions, and extended to systems with constraints and non-conservative forcing or dissipation. Variational Runge–Kutta discretizations are...
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This paper will review recent advances in the formulation of a discrete version of geometric mechanics, based on the discretization of Hamilton’s variational principle, and progress that has been made in reduction theory for discrete variational mechanics in the form of Discrete Routh Reduction. To place discrete geometric mechanics on a firm mathematical foundation, we propose to develop a dis...
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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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Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The modern vision of mechanics includes, besides the traditional mechanics of particles and rigid bodies, field theories such as electromagnetism, fluid mechanics, plasma physics, solid mechanics as well as quantum mechanics, ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2006
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/39/19/s12