Abstract
For certain nonholonomic and holonomic mechanical systems we have obtained the existence conditions for the particular integral being a linear bundle of the Hamiltonian and the momenta. The conditions are simplified for a certain class of holonomic systems, containing the well-known [1] case of the particular Jacobi integral. An example of the fulfillment of these conditions is a variant of the restricted problem of translation-rotational motion of a gyrostat in a Newtonian force field.
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