The problem of metrizability of dynamical systems that admit normal shift

The problem of metrizability of dynamical systems that admit normal shift is formulated and solved. The explicit form of the force field for a Newtonian dynamical system _ttr=F(r, _tr) along which normal shift coincides with the metric normal shift for some conformally Euclidean metric is found.State University, Bashkir. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 85–93, October, 1994.