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In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-calledČaplygin systems. 2000 Mathematics Subject Classification. 70H20, 37J60, 70F25.doi:10.1088/1751-8113/41/1/015205 fatcat:zz2b4xu2ynhe7l2n2wu5mutuom