Abstract
The question of the longitudinal bending of a rod consisting of rigid links connected by hinges is being studied. It is shown that, as in the classical version of a solid rod, the problem can be posed as a variational minimum energy problem, but given by a functional defined on a class of functions with a discrete domain of definition. The main provisions of the classical calculus of variations are transferred to functionals of this type: the formula of variation is found, a generalization of the main lemma of the calculus of variations is proved, an analogue of the Euler equation, which is a difference equation, is obtained. Applying the results obtained and the known properties of classical difference equations, we succeeded in solving an analogue of the Euler problem for two types of a hinge rod: for a rod consisting of links of the same length, and for an arbitrary choice of lengths of links. In both cases we find the critical Euler force, as well as the equation and the form of the deflection curve.
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