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Start Over Coverage 291-328

2. The symmetry reduction of variational integrals

Creator:
Tryhuk, Václav and Chrastinová, Veronika
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Routh reduction, Lagrange variational problem, Poincaré-Cartan form, diffiety, standard basis, controllability, and variation
Language:
English
Description:
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined systems of ordinary differential equations, Poincaré-Cartan forms, variations and extremals is involved for the preparation of the main task. The self-contained exposition differs from the common actual theories and rests only on the most fundamental tools of classical mathematical analysis, however, they are applied in infinite-dimensional spaces. The article may be of a certain interest for nonspecialists since all concepts of the calculus of variations undergo a deep reconstruction.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public