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Optimal trajectories which are tangent to an affine distribution
Author(s) -
Popescu Mihai,
Pelletier Fernand
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701029
Subject(s) - tangent bundle , tangent , affine transformation , manifold (fluid mechanics) , mathematics , bundle , unit tangent bundle , affine connection , parallelizable manifold , tangent space , normal bundle , work (physics) , distribution (mathematics) , pure mathematics , mathematical analysis , geometry , physics , vector bundle , engineering , materials science , composite material , mechanical engineering , thermodynamics
In this work we study the trajectories which are tangent to an affine sub‐bundle in the tangent bundle of a manifold and which minimize the “total energy”.We give some characterizations of such “regular” trajectories in terms of control theory and geometrical theory. We also build some sufficient conditions of existence for such curves. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)