Dynamics of Systems Under Elastic Constraints

Abstract

In the present chapter we extend to dynamical problems the representations of constraints in terms of force fields that were discussed earlier in Secs.2.3–2.5. In mechanical problems, constraints are caused by real deformable bodies and the reactions of such constraints are defined by physical properties of bodies causing these constraints. The constraint equations ф (x)=0 or constraint inequalities ф (x) ≤ 0, known as bilateral or unilateral constraints, indicate only the geometrical form of the unloaded constraints. And the concept of an ideal rigid constraint is connected with such abstract models of real bodies as a perfectly rigid body or an incompressible fluid. Undoubtedly, useful applications of the idealized models of the natural objects have their own limitations, and it is desirable to determine the extent of these limitations. We must also clarify what analytical difficulties cause complication in investigating the given object and what difficulties are the result of model not conforming to the real object. The first to note the necessity of representing constraints by strong force fields was, apparently, Johann Bernoulli [53]*.