The linearization of equilibria of Hamiltonian systems is Hamiltonian; this has well-known and important implications for the spectrum. The analogous statement for nonholonomic systems is provided. It follows, for example, that the linearization of the ground state of a nonholonomic system is always Hamiltonian.
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Patrick, G.W. The intrinsic linearization of equilibria of nonholonomic systems. Lett Math Phys 108, 2487–2490 (2018). https://doi.org/10.1007/s11005-018-1089-5