In this paper a dynamical system with n degrees of freedom is considered, under the action of forces depending not only on the coordinates and time, but also on the lagrangian velocities and the accelerations, for which there is the lagrangian function or a kinetic potential, so that the equations of motion are reducible to the canonical form. If the forces have a linear component in the lagrangian velocities, this component has a gyrostatic character. If the lagrangian function has terms of the second degree in the lagrangian velocities, the corresponding forces depend on the accelerations. An application is given to the motion of an electrically charged particle in a magnetic field, attracted by a fixed point according to a law generalising the Weber electrodynamics.