A complete solution of the well-known Mayer’s problem, which is concerned with the possibility of extending Hamilton’s principle expressed in the form valid for conservative dynamical systems to one special case of nonconservative systems (Appell, 1911), is obtained. Namely, the necessary and sufficient conditions which have to be satisfied by the coefficients of the given nonconservative generalized forces so that the Mayer’s potential (and, as a consequence, the descriptive function of the system) can be constructed, are established. This result is illustrated by an example.

Appell, P., 1911, Traite´ de me´canique rationnelle, T. II, Gauthier-Villars, Paris, pp. 440–441.
Merkin, D. R., 1956, Gyroscopic Systems, Gostechizdat, Moscow, pp. 17–20; 52–54.
Pars, L. A., 1965, A Treatise on Analytical Dynamics, Heinemann, London, pp. 81–82.
Santilli, R. M., 1978, Foundations of Theoretical Mechanics, I, Springer-Verlag, New York.
Santilli, R. M., 1983, Foundations of Theoretical Mechanics, II, Springer-Verlag, New York, p. 3.
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