Abstract

It is shown that the solution of certain problems of the dynamics appropriate and often the only acceptable is the presentation of the state of the object in a superposition of its boundary conditions, and the intermediate state depends on the values of state functions that characterize the variability of the state of the object. It was noted that in many cases are non-linear function of the state, and their analytical representation often unknown, but for the model with mutually by equal boundary conditions state function, as a rule, are continuous and monotone on the interval studied, and the value of state functions varies from zero to unity; under these conditions, the state function in almost any way are investigated for the analytical range and can be represented as a series expansions, for example Taylor. It is shown that the characteristic type of practical problems which can be solved using the proposed method is to calculate the dynamics of bulk cargo platform in the commission of linear oscillations in a horizontal plane; main difficulty of this problem is the lack of even approximate data on dynamic friction coefficient of the generalized because its value significantly affect fragments move cargo in its entirety, and not only in the plane of contact with the platform. It is shown that the representation of the cargo as a superposition of its movable and stationary states can solve this and similar problems.

Keywords

Superposition, the boundary condition, function of the state, the state variable.