Peculiarities of the use of acceleration-dependent forces in mechanical problems

Abstract

Until very recently, the wrong belief that given forces in mechanics cannot depend on acceleration was a wide-spread opinion. As a consequence, little effort, if any, has been made to develop a formal mechanical theory for such forces. At the present time, a class of new problems involving the study of mechanical systems acted on by forces that depend on acceleration and higher derivatives can be considered on the basis of traditional statements of mechanical problems (of stabilization, stability, optimal control, etc.). The current paper is primarily devoted to equilibrium stabilization using acceleration-dependent forces. For definiteness, the analysis is concerned with the tilting railway car, which is a mechanical system where the use of such forces is indispensable. In spite of the specificity of this system, the analysis allows one to get an idea of the generalities of the use of acceleration-dependent forces in mechanics and shows that they can be used in practice to good advantage.