The known models of contactless vehicles are usually described by low order equations. This is caused by insuperable problems in obtaining analytical solutions for the nonlinear equations of higher than second order. In real contactless suspension systems the generalized coordinate may depend on many variables, each of which is described by a multivariate differential equation. In this case the only way to go from the initial nonlinear model to  an integrable one is linearization.
One of the known methods of linearization of nonlinear models is the substitution of the argument of a nonlinear function by a known function of time with subsequent definition of linearization factors. Such method is applied, for example, for harmonic linearization of nonlinear functions. A similar approach is used in the present article.
The article offers a model of a contactless vehicle in which the nonlinearity of power action is approximated by a variable factor of hyperbolic type. The model of nonlinearity depends on time and on the rotor speed as a parameter. The model of a contactless suspension may be treated as a model of a linear nonstationary control system with a singularity.
The model can be used for the analysis and synthesis of control systems of gyroscopes and contactless vehicles.