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The mechanics of rigid bodies in Cartesian space.
Up to the dynamics of the center of mass?, this is the special case of Hamiltonian dynamics on Lie groups for the case of the special orthogonal group $SO(n)$.
Often this is considered (only) for $n = 3$, which is the case pertaining to rigid bodies in observable nature, hence using SO(3).
Hamiltonian dynamics on Lie groups
rigid body dynamics
A general introduction is in section 1.1d of
A discussion from the more general perspective of Hamiltonian dynamics on Lie groups is in section 4.4 of
Vladimir Arnol'd, Mathematical methods of classical mechanics, Springer 1989 (section 28)
Landau-Lifschitz, vol.1, Mechanics
R. Abraham, J. Marsden: The Foundations of Mechanics, Benjamin Press, 1967, Addison-Wesley, 1978; large pdf 86 Mb free at CaltechAuthors
A discussion of rigid body dynamics as a special case of the general Euler-Arnold equation is at
References from the point of view of Geometric Algebra include
David Hestenes, Rotational dynamics with geometric algebra (web)
Terje Vold, An introduction to geometric algebra with an application to rigid body mechanics (pdf)
Discussion of (geometric) quantization of rigid bodies is in