Problems and progress in nonholonomic reduction (Q1853805)

The present paper is an excellent survey on analogies between Hamiltonian and nonholonomic systems, with a special view to reduction schemes in presence of symmetry. Several citations are from the historical founders of the subject, e.g. Appell (1899), Chaplygin (around the same time), Jacobi (1837, 1842), Liouville (1855), Arnold (1865), Meyer (1973), Marsden and Weinstein (1974), and also from the recent papers of the author et al. [for example Rep. Math. Phys. 42, No. 1-2, 231--247 (1998; Zbl 0931.37022) and Rep. Math. Phys. 37, No. 1-3, 295--308 (1996; Zbl 0887.58016)]. The paper begins with two examples, one physical (the rattleback) and one mathematical, and ends with a list of five open problems which offers good starting points for a future research.