S. V. Bogoslovsky
Saint-Petersburg State University of Aerospace Instrumentation
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.