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30 K. HU¨PER, K.A. KRAKOWSKI AND F. SILVA LEITE
[5] Knut Hu¨per, Martin Kleinsteuber, and F´atima Silva Leite. Rolling Stiefel manifolds. Inter- national Journal of Systems Science, 39(8):881–887, 2008.
[6] Knut Hu¨per and F´atima Silva Leite. On the geometry of rolling and interpolation curves on Sn, SOn and Graßmann manifolds. Journal of Dynamical and Control Systems, 13(4):467– 502, October 2007.
[7] Shoshichi Kobayashi. Transformation Groups in Di↵erential Geometry, volume 70 of Ergeb- nisse der Mathematik und ihrer Grenzgebiete. Springer, 1972. 182 pages.
[8] John M. Lee. Riemannian Manifolds: An Introduction to Curvature. Number 176 in Graduate Texts in Mathematics. Springer-Verlag, New York, 1997.
[9] Richard M. Murray, S.Shankar Sastry, and Zexiang Li. A mathematical introduction to robotic manipulation. Boca Raton, FL: CRC Press. xix, 456 p., 1994.
[10] Katsumi Nomizu. Kinematics and di↵erential geometry of submanifolds. Toˆhoku Math. Journ., 30:623–637, 1978.
[11] Richard W. Sharpe. Di↵erential Geometry: Cartan’s Generalization of Klein’s Erlangen Pro- gram. Number 166 in Graduate Texts in Mathematics. Springer-Verlag, New York, 1997.
[12] F´atima Silva Leite and Krzysztof Andrzej Krakowski. Covariant di↵erentiation under rolling maps. In Pr´e-Publicac¸o˜es do Departamento de Matema´tica, number 08-22, pages 1–8. Uni- versity of Coimbra, 2008.
[13] Wolfram Research, Inc. Mathematica 8.0, 2010.
[14] Jason Zimmerman. Optimal control of the sphere Sn rolling on En. Mathematics of Control,
Signals, and Systems, 17(1):14–37, 2005.
(K. Hu¨per) Institute for Mathematics
University of Wu¨rzburg
Germany
E-mail address: hueper@mathematik.uni-wuerzburg.de
(K.A. Krakowski) School of Science & Technology University of New England
Australia
E-mail address: kris@mcs.une.edu.au
(F. Silva Leite) Department of Mathematics and Institute of Systems and Robotics University of Coimbra
Portugal
E-mail address: fleite@mat.uc.pt