Abstract
In this paper we study the Jacobiator (the cyclic sum that vanishes when the Jacobi identity holds) of the almost Poisson brackets describing nonholonomic systems. We revisit the local formula for the Jacobiator established by Koon and Marsden (Rep Math Phys 42:101–134, 1998) using suitable local coordinates and explain how it is related to the global formula obtained in Balseiro (Arch. Ration. Mech. Anal. 214(2):453-501, 2014), based on the choice of a complement to the constraint distribution. We use an example to illustrate the benefits of the coordinate-free viewpoint.
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Acknowledgements
I thank the organizers of the Focus Program on Geometry, Mechanics and Dynamics, the Legacy of Jerry Marsden, held at the Fields Institute in Canada, for their hospitality during my stay. I also benefited from the financial support given by Mitacs (Canada), and I am specially grateful to Jair Koiller for his help. I also thank FAPERJ (Brazil) and the GMC Network (projects MTM2012-34478, Spain) for their support. I finally acknowledge CAPES (Brazil) for the financial support through the grant CsF PVE 11/2012.
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Dedicated to the memory of J.E. Marsden
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Balseiro, P. (2015). A Global Version of the Koon-Marsden Jacobiator Formula. In: Chang, D., Holm, D., Patrick, G., Ratiu, T. (eds) Geometry, Mechanics, and Dynamics. Fields Institute Communications, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2441-7_1
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DOI: https://doi.org/10.1007/978-1-4939-2441-7_1
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