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May 31, 2011 at 20:38 comment added Beni Bogosel @Giuseppe: Thank you for the reference.
May 31, 2011 at 19:06 comment added agt Dear Beni Bogosel you could give a look to "Nonholonomic Mechanics and Control" by A.Bloch.
May 31, 2011 at 18:57 comment added agt Dear jkersch: it could be helpful for someone starting to learn analysis on manifolds, to see the product formula (cf. for example Abraham, Marsden, Ratiu MTA) as justification of the interpretation you give of the Lie bracket of vector fields. I believe that this interpretation is not always presented in introductory texts to smooth manifolds.
May 31, 2011 at 18:52 comment added Beni Bogosel Thank you for your answer. I begin to understand how things work in the asked question. I would be interested in some other applications of differential geometry, similar to this one. Any reference would be helpful.
May 31, 2011 at 18:48 vote accept Beni Bogosel
May 31, 2011 at 18:35 history answered jvkersch CC BY-SA 3.0