The periodic laws of motion of a real mechanism imply the periodicity of all dynamic characteristics of the mechanism during such a movement, including the elastic displacements of its constituent links. This statement covers the most difficult problem of the dynamics of an elastically deformable body. However the existing publications devoted to the study of flexible mechanisms do not mention the periodicity of elastic displacements of the links when the mechanisms move according to periodic laws. This article discusses the periodicity and pseudo-periodicity of the elastic displacements of the links using examples of calculations of the motion of a double pendulum and a slider–crank mechanism without taking into account dissipative forces.
Generalize method of iteration is proposed, presented as a combination of the classical iteration and proportional division methods, on which the conditions of Boltsano-Cochy theorems are satisfied. Аn evidence of the proposed algorithm's convergence is brought.Originally, the compression reflection operator as a function from one variable is considered.
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