Citation: |
[1] |
R. Abraham and J. E. Marsden, "Foundations of Mechanics," 2^{nd} edition, Benjamin/Cummings Publishing Co., Inc., Reading, MA, 1978. |
[2] |
V. I. Arnol'd, "Mathematical Methods of Classical Mechanics," 2^{nd} edition, Graduate Texts in Mathematics, 60, Springer Verlag, New York, 1989. |
[3] |
A. M. Bloch, J. Ballieul, P. E. Crouch and J. E. Marsden, "Nonholonomic Mechanics and Control," number 24 in "Interdisciplinary Texts in Mathematics," Springer Verlag, New York, 2003. |
[4] |
A. M. Bloch, P. E. Crouch, D. D. Holm and J. E. Marsden, An optimal control formulation for inviscid incompressible ideal fluid flow, In "Proc. IEEE Conf. on Decision and Control," Sydney, Australia, (December 2000), 1273-1279, arXiv:nlin/0103042. |
[5] |
A. M. Bloch, P. E. Crouch, J. E. Marsden and T. S. Ratiu, The symmetric representation of the rigid body equations and their discretization, Nonlinearity, 15 (2002), 1309-1341.doi: 10.1088/0951-7715/15/4/316. |
[6] |
A. M. Bloch, P. E. Crouch, J. E. Marsden and A. K. Sanyal, Optimal control and geodesics on quadratic matrix Lie groups, Foundations of Computational Mathematics, 8 (2008), 469-500.doi: 10.1007/s10208-008-9025-1. |
[7] |
A. M. Bloch, P. E. Crouch and A. K. Sanyal, A variational problem on Stiefel manifolds, Nonlinearity, 19 (2006), 2247-2276.doi: 10.1088/0951-7715/19/10/002. |
[8] |
Y. N. Federov and V. V. Kozlov, Various aspects of n-dimensional rigid body dynamics, in "Dynamical Systems in Classical Mechanics," American Mathematical Society Translations, 168, Amer. Math. Soc., Providence, RI, (1995), 141-171. |
[9] |
F. Gay-Balmaz and T. S. Ratiu, Clebsch optimal control formulation in mechanics, preprint. |
[10] |
I. M. Gelfand and S. V. Fomin, "Calculus of Variations," Prentice-Hall, Inc., Englewood Cliffs, NJ, (reprinted by Dover, 2000), 1963. |
[11] |
D. D. Holm, Riemannian optimal control formulation of incompressible ideal fluid flow, preprint. |
[12] |
D. E. Kirk, "Optimal Control Theory: An Introduction," Dover Publications, New York, 2004. |
[13] |
S. V. Manakov, Note on the integration of Euler's equations of the dynamics of an n-dimensional rigid body, Functional Analysis and Its Applications, 10 (1976), 328-329.doi: 10.1007/BF01076037. |
[14] |
J. E. Marsden and T. S. Ratiu, "Introduction to Mechanics and Symmetry," 2^{nd} edition, Texts in Applied Mathematics, 17, Springer Verlag, New York, 1999. |
[15] |
A. S. Mischenko and A. T. Fomenko, On the integration of the Euler equations on semisimple Lie algebras, Sov. Math. Dokl., 17 (1976), 1591-1593. |
[16] |
T. S. Ratiu, The motion of the free n-dimensional rigid body, Indiana University Mathematics Journal, 29 (1980), 609-629.doi: 10.1512/iumj.1980.29.29046. |