المؤلفون: Bartoň, Stanislav

مصطلحات موضوعية: keyword:momentum of force, keyword:momentum of inertia, keyword:nonlinear differential equation, keyword:Maple, msc:34A34, msc:68U20, msc:70B10

وصف الملف: application/pdf

الاتاحة: http://hdl.handle.net/10338.dmlcz/703063

المؤلفون: Krakowski, Krzysztof Andrzej, Leite, Fátima Silva

مصطلحات موضوعية: msc:35B06, msc:53A05, msc:53B21, msc:58E10, msc:70B10

وصف الملف: application/pdf

Relation: zbl:Zbl 06707385

الاتاحة: http://hdl.handle.net/10338.dmlcz/146744

المؤلفون: Krakowski, Krzysztof Andrzej, Silva Leite, Fátima

مصطلحات موضوعية: keyword:ellipsoid, keyword:rolling maps, keyword:Gaussian curvature, keyword:geodesics, keyword:hypersurface, msc:35B06, msc:53A05, msc:53B21, msc:58E10, msc:70B10

وصف الملف: application/pdf

Relation: mr:MR3501158; zbl:Zbl 1374.53033; reference:[1] Bicchi, A., Sorrentino, R., Piaggio, C.: Dexterous manipulation through rolling.In: ICRA'95, IEEE Int. Conf. on Robotics and Automation 1995, pp. 452-457. 10.1109/robot.1995.525325; reference:[2] Borisov, A. V., Mamaev, I. S.: Isomorphism and Hamilton representation of some nonholonomic systems.Sibirsk. Mat. Zh. 48 (2007), 1, 33-45. Zbl 1164.37342, MR 2304876, 10.1007/s11202-007-0004-6; reference:[3] Borisov, A. V., Mamaev, I. S.: Rolling of a non-homogeneous ball over a sphere without slipping and twisting.Regular and Chaotic Dynamics 12 (2007), 2, 153-159. Zbl 1229.37081, MR 2350303, 10.1134/s1560354707020037; reference:[4] Borisov, A. V., Mamaev, I. S.: Isomorphisms of geodesic flows on quadrics.Regular and Chaotic Dynamics 14 (2009), 4 - 5, 455-465. Zbl 1229.37096, MR 2551869, 10.1134/s1560354709040030; reference:[5] Caseiro, R., Martins, P., Henriques, J. F., Leite, F. Silva, Batista, J.: Rolling Riemannian manifolds to solve the multi-class classification problem.In: CVPR 2013, pp. 41-48. 10.1109/cvpr.2013.13; reference:[6] Chavel, I.: Riemannian Geometry - A Modern Introduction. Second edition.Cambridge Studies in Advanced Mathematics, No. 98. Cambridge University Press, Cambridge 2006. MR 2229062, 10.1017/cbo9780511616822; reference:[7] Crouch, P., Leite, F. Silva: Rolling maps for pseudo-Riemannian manifolds.In: Proc. 51th IEEE Conference on Decision and Control, (Hawaii 2012). 10.1109/cdc.2012.6426140; reference:[8] Fedorov, Y. N., Jovanović, B.: Nonholonomic LR systems as generalized Chaplygin systems with an invariant measure and flows on homogeneous spaces.J. Nonlinear Science 14 (2004), 4, 341-381. Zbl 1125.37045, MR 2076030, 10.1007/s00332-004-0603-3; reference:[9] Hüper, K., Krakowski., K. A., Leite, F. Silva: Rolling Maps in a Riemannian Framework.Textos de Matemática 43, Department of Mathematics, University of Coimbra 2011, pp. 15-30. MR 2894254; reference:[10] Hüper, K., Leite, F. Silva: On the geometry of rolling and interpolation curves on $S^n$, $SO_n$ and Graßmann manifolds.J. Dynam. Control Systems 13 (2007), 4, 467-502. MR 2350231, 10.1007/s10883-007-9027-3; reference:[11] Prete, N. M. Justin Carpentier J.-P. L. Andrea Del: An analytical model of rolling contact and its application to the modeling of bipedal locomotion.In: Proc. IMA Conference on Mathematics of Robotics 2015, pp. 452-457.; reference:[12] Kato, T.: Perturbation Theory for Linear Operators.Springer-Verlag, Classics in Mathematics 132, 1995. Zbl 0836.47009, MR 1335452, 10.1007/978-3-642-66282-9; reference:[13] Knörrer, H.: Geodesics on the ellipsoid.Inventiones Mathematicae 59 (1980), 119-144. Zbl 0431.53003, MR 0577358, 10.1007/bf01390041; reference:[14] Knörrer, H.: Geodesics on quadrics and a mechanical problem of C. Neumann.J. für die reine und angewandte Mathematik 334 (1982), 69-78. 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MR 1468735; reference:[19] Moser, J.: Three integrable Hamiltonian systems connected with isospectral deformations.Advances Math. 16 (1975), 2, 197-220. Zbl 0303.34019, MR 0375869, 10.1016/0001-8708(75)90151-6; reference:[20] Moser, J.: Geometry of quadrics and spectral theory.In: The Chern Symposium 1979 (W.-Y. Hsiang, S. Kobayashi, I. Singer, J. Wolf, H.-H. Wu, and A. Weinstein, eds.), Springer, New York 1980, pp. 147-188. Zbl 0455.58018, MR 0609560, 10.1007/978-1-4613-8109-9_7; reference:[21] Nomizu, K.: Kinematics and differential geometry of submanifolds.Tôhoku Math. J. 30 (1978), 623-637. Zbl 0395.53005, MR 0516894, 10.2748/tmj/1178229921; reference:[22] Okamura, A. M., Smaby, N., Cutkosky, M. R.: An overview of dexterous manipulation.In: ICRA'00, IEEE Int Conf. on Robotics and Automation 2000, pp. 255–262. DOI:10.1109/robot.2000.844067 10.1109/robot.2000.844067; reference:[23] Raţiu, T.: The C. Neumann problem as a completely integrable system on an adjoint orbit.Trans. Amer. Math. Soc. 264 (1981), 2, 321-329. Zbl 0475.58006, MR 0603766, 10.1090/s0002-9947-1981-0603766-3; reference:[24] Sharpe, R. W.: Differential Geometry: Cartan's Generalization of Klein's Erlangen Program.Springer-Verlag, Graduate Texts in Mathematics 166, New York 1997. Zbl 0876.53001, MR 1453120; reference:[25] Leite, F. Silva, Krakowski, K. A.: Covariant differentiation under rolling maps.In: Pré-Publicações do Departamento de Matemática, No. 08-22, University of Coimbra 2008, pp. 1-8.; reference:[26] Spivak, M.: Calculus on Manifolds.Mathematics Monograph Series, Addison-Wesley, New York 1965. Zbl 0381.58003; reference:[27] Uhlenbeck, K.: Minimal 2-spheres and tori in $S^k$.Preprint, 1975.; reference:[28] Veselov, A. P.: A few things I learnt from Jürgen Moser.Regular and Chaotic Dynamics 13 (2008), 6, 515-524. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/145771

المؤلفون: Krakowski, Krzysztof, Silva Leite, Fátima

مصطلحات موضوعية: keyword:rolling, keyword:group of isometries, keyword:ellipsoid, keyword:kinematic equations, keyword:interpolation, msc:41A05, msc:53B21, msc:53C22, msc:65D05, msc:65D07, msc:65D10, msc:70B10

وصف الملف: application/pdf

Relation: mr:MR3275084; zbl:Zbl 06386426; reference:[1] Agrachev, A., Sachkov, Y.: Control Theory from the Geometric Viewpoint.In: Encyclopaedia of Mathematical Sciences 87 (2004), Springer-Verlag. Zbl 1062.93001, MR 2062547; reference:[2] Camarinha, M.: The Geometry of Cubic Polynomials on Riemannian Manifolds.PhD. Thesis, Departamento de Matemática, Universidade de Coimbra 1996.; reference:[3] Crouch, P., Kun, G., Leite, F. S.: The De Casteljau algorithm on Lie groups and spheres.J. Dyn. Control Syst. 5 (1999), 3, 397-429. Zbl 0961.53027, MR 1706785, 10.1023/A:1021770717822; reference:[4] Crouch, P, Leite, F. S.: Geometry and the dynamic interpolation problem.In: Proc. American Control Conference Boston 1991, pp. 1131-1137.; reference:[5] Crouch, P., Leite, F. S.: The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces.J. Dyn. Control Syst. 1 (1995), 2, 177-202. Zbl 0946.58018, MR 1333770, 10.1007/BF02254638; reference:[6] Fedorov, Y. N., Jovanović, B.: Nonholonomic LR systems as generalized chaplygin systems with an invariant measure and flows on homogeneous spaces.J. Nonlinear Sci. 14 (2004), 4, 341-381. Zbl 1125.37045, MR 2076030, 10.1007/s00332-004-0603-3; reference:[7] Giambó, R., Giannoni, F., Piccione, P.: Fitting smooth paths to spherical data.IMA J. Math. Control Inform. 19 (2002), 445-460. MR 1949013; reference:[8] Hüper, K., Kleinsteuber, M., Leite, F. S.: Rolling Stiefel manifolds.Int. J. Systems Sci. 39 (2008), 8, 881-887. Zbl 1168.53007, MR 2437853; reference:[9] Hüper, K., Krakowski, K. A., Leite, F. S.: Rolling Maps in a Riemannian Framework.In: Mathematical Papers in Honour of Fátima Silva Leite, Textos de Matemática 43, Department of Mathematics, University of Coimbra 2011, pp. 15-30. Zbl 1254.53018, MR 2894254; reference:[10] Hüper, K., Leite, F. S.: Smooth interpolating curves with applications to path planning.In: 10th IEEE Mediterranean Conference on Control and Automation (MED 2002), Lisbon 2002.; reference:[11] Hüper, K., Leite, F. S.: On the geometry of rolling and interpolation curves on $S^n$, $SO_n$ and Graßmann manifolds.J. Dyn. Control Syst. 13 (2007), 4, 467-502. MR 2350231, 10.1007/s10883-007-9027-3; reference:[12] Jupp, P., Kent, J.: Fitting smooth paths to spherical data.Appl. Statist. 36 (1987), 34-46. Zbl 0613.62086, MR 0887825, 10.2307/2347843; reference:[13] Jurdjevic, V., Zimmerman, J.: Rolling problems on spaces of constant curvature.In: Lagrangian and Hamiltonian methods for nonlinear control 2006, Proc. 3rd IFAC Workshop 2006 (F. Bullo and K. Fujimoto, eds.), Nagoya 2007, Lect. Notes Control Inform. Sciences, Springer, pp. 221-231. Zbl 1136.49028, MR 2376942; reference:[14] Krakowski, K., Leite, F. S.: Smooth interpolation on ellipsoids via rolling motions.In: PhysCon 2013, San Luis Potosí, Mexico 2013.; reference:[15] Krakowski, K. A., Leite, F. S.: Why controllability of rolling may fail: a few illustrative examples.In: Pré-Publicações do Departamento de Matemática, No. 12-26, University of Coimbra 2012, pp. 1-30.; reference:[16] Lee, J. M.: Riemannian Manifolds: An Introduction to Curvature.In? Graduate Texts in Mathematics No. 176, Springer-Verlag, New York 1997. Zbl 0905.53001, MR 1468735; reference:[17] Machado, L., Leite, F. S., Krakowski, K.: Higher-order smoothing splines versus least squares problems on riemannian manifolds.J. Dyn. Control Syst. 16 (2010), 1, 121-148. Zbl 1203.65028, MR 2580471, 10.1007/s10883-010-9080-1; reference:[18] Noakes, L., Heinzinger, G., Paden, B.: Cubic splines on curved spaces.IMA J. Math. Control Inform. 6 (1989), 465-473. Zbl 0698.58018, MR 1036158, 10.1093/imamci/6.4.465; reference:[19] Nomizu, K.: Kinematics and differential geometry of submanifolds.Tôhoku Math. J. 30 (1978), 623-637. Zbl 0395.53005, MR 0516894, 10.2748/tmj/1178229921; reference:[20] Park, F., Ravani, B.: Optimal control of the sphere ${S^n}$ rolling on ${E^n}$.ASME J. Mech. Design 117 (1995), 36-40.; reference:[21] Samir, C., Absil, P.-A., Srivastava, A., Klassen, E.: A gradient-descent method for curve fitting on Riemannian manifolds.Found. Comput. Math. 12 (2012), 49-73. Zbl 1245.65017, MR 2886156, 10.1007/s10208-011-9091-7; reference:[22] Sharpe, R. W.: Differential Geometry: Cartan's Generalization of Klein's Erlangen Program.In: Graduate Texts in Mathematics, No. 166. Springer-Verlag, New York 1997. Zbl 0876.53001, MR 1453120; reference:[23] Zimmerman, J.: Optimal control of the sphere ${S^n}$ rolling on ${E^n}$.Math. Control Signals Systems 17 (2005), 1, 14-37. Zbl 1064.49021, MR 2121282, 10.1007/s00498-004-0143-2

الاتاحة: http://hdl.handle.net/10338.dmlcz/143983

المؤلفون: Modugno, Marco, Vitolo, Raffaele

مصطلحات موضوعية: keyword:classical mechanics, keyword:rigid system, keyword:Newton’s law, keyword:Riemannian geometry, msc:37Jxx, msc:70B10, msc:70Bxx, msc:70Exx, msc:70Fxx, msc:70G45

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/108065

المؤلفون: Chudý, Jaroslav

مصطلحات موضوعية: msc:70B10, msc:70B99

وصف الملف: application/pdf

Relation: mr:MR0388896; zbl:Zbl 0329.70003; reference:[1] Chudý J.: Beitrag zur kinematischen Synthese bei gegebener Polkonfiguration.Aplikace matematiky, 19 (1974), ČSAV, Praha. MR 0347180; reference:[2] Pírko Z.: Úvod do kinematické geometrie.SNTL, Praha, 1968.; reference:[3] Loria G.: Ebene Kurven II.1910.

الاتاحة: http://hdl.handle.net/10338.dmlcz/103612