[1] Abraham R. Marsden J E.Foundations of Mechanics. Reading, MA: Addison-Wesley, 1978 [2] Abraham R, Marsden J E, Ratiu T S.Manifolds, Tensor Analysis and Applications. New York: Springer- Verlag, 1988 [3] Arnold V I.Mathematical Methods of Classical Mechanics. New York: Springer-Verlag, 1989 [4] Marsden J E, Ratiu T S.Introduction to Mechanics and Symmetry. New York: Springer-Verlag, 1999 [5] Woodhouse N M J. Geometric Quantization. Oxford: Clarendon Press, 1992 [6] Ge Z, Marsden J E.Lie-Poisson integrators and Lie-Poisson Hamilton-Jacobi theory. Phys Lett A, 1988, 133: 134-139 [7] Lázaro-Camí J A. Ortega J P. The stochastic Hamilton-Jacobi equation. J Geom Mech, 2009, 1: 295-315 [8] Marsden J E, Wang H, Zhang Z X.Regular reduction of controlled Hamiltonian system with symplectic structure and symmetry. Diff Geom Appl, 2014, 33(3): 13-45 [9] Cariñena J F, Gràcia X, Marmo G, et al. Geometric Hamilton-Jacobi theory. Int J Geom Methods Mod Phys, 2006, 3: 1417-1458 [10] Cariñena J F, Gràcia X, Marmo G, et al. Geometric Hamilton-Jacobi theory for nonholonomic dynamical systems. Int J Geom Methods Mod Phys, 2010, 7: 431-454 [11] Wang H.Hamilton-Jacobi theorems for regular reducible Hamiltonian system on a cotangent bundle. J Geom Phys, 2017, 119: 82-102 [12] Libermann P, Marle C M.Symplectic Geometry and Analytical Mechanics. Dordrecht: Springer, 1987 [13] Marsden J E.Lectures on Mechanics. Cambridge: Cambridge University Press, 1992 [14] Ortega J P, Ratiu T S.Momentum Maps and Hamiltonian Reduction. Boston: Birkhäuser, 2004 [15] León M, Rodrigues P R.Methods of Differential Geometry in Analytical Mechanics. Amsterdam: North- Holland, 1989 [16] Marsden J E, Misiolek G, Ortega J P, et al.Hamiltonian Reduction by Stages. Berlin: Springer, 2007 [17] Marsden J E, Montgomery R, Ratiu T S.Reduction, Symmetry and Phases in Mechanics. Providence, RI: American Mathematical Society, 1990 [18] Marsden J E, Perlmutter M.The orbit bundle picture of cotangent bundle reduction. C R Math Acad Sci Soc R Can, 2000, 22: 33-54 [19] Marsden J E, Weinstein A.Reduction of symplectic manifolds with symmetry. Rep Math Phys, 1974, 5: 121-130 [20] Meyer K R.Symmetries and integrals in mechanics//Peixoto M. Dynamical Systems. New York: Academic Press, 1973: 259-273 [21] Nijmeijer H, Van der Schaft A J. Nonlinear Dynamical Control Systems. New York: Springer-Verlag, 1990 [22] Wang H, Zhang Z X.Optimal reduction of controlled Hamiltonian system with Poisson structure and symmetry. J Geom Phys, 2012, 62(5): 953-975 [23] Ratiu T S, Wang H.Poisson reduction by controllability distribution for a controlled Hamiltonian system. arXiv: 1312.7047 [24] Wang H.Some developments of reduction theory for controlled Hamiltonian system with symmetry (in Chinese). Sci Sin Math, 2018, 48: 1-12 [25] Wang H.Reductions of controlled Hamiltonian system with symmetry//Bai C M, Gazeau J P, Ge M L, et al. Symmetries and Groups in Contemporary Physics. Singapore: World Scientific, 2013: 639-642 [26] Marle C M.Symplectic manifolds, dynamical groups and Hamiltonian mechanics//Cahen M, Flato M. Differential Geometry and Relativity. Dordrecht: Reidel Publ Co, 1976: 249-269 [27] Kazhdan D, Kostant B, Sternberg S.Hamiltonian group actions dynamical systems of Calogero type. Comm Pure Appl Math, 1978, 31: 481-508 [28] Krishnaprasad P S, Marsden J E.Hamiltonian structure and stability for rigid bodies with flexible attachments. Arch Rational Mech Anal, 1987, 98: 71-93 [29] León M, Wang H. Hamilton-Jacobi equations for nonholonomic reducible Hamiltonian systems on a cotangent bundle. arXiv:1508.07548(v3) [30] Wang H.Hamilton-Jacobi equations for nonholonomic magnetic Hamiltonian systems. Commun Math Res, 2022, 38(3): 351-388 [31] Wang H.Dynamical equations of the controlled rigid spacecraft with a rotor. arXiv: 2005.02221 [32] Wang H. Symmetric reduction and Hamilton-Jacobi equations for the controlled underwater vehicle-rotor system. arXiv:1310.3014(v3) |