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IssuesArchive of Issues2005-6pp.128-142

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A. P. Leutin, "Modeling the motion of bodies connected by friction joints," Mech. Solids. 40 (6), 128-142 (2005)
Year 2005 Volume 40 Number 6 Pages 128-142
Title Modeling the motion of bodies connected by friction joints
Author(s) A. P. Leutin (Zhukovskii)
Abstract We consider the motion of complex mechanical systems consisting of a carrier and weights connected to it by joints. We develop an approach permitting one to solve the dynamic equations of the system for the accelerations of individual bodies in closed form, thus providing considerable economy in the number of arithmetic operations compared with the approaches based on standard numerical methods. On the basis of similarity theory, we obtain simple approximations for computing the size of the joint contact region. In view of the dependence of the Coulomb friction coefficient on the contact pressure, we determine the friction force and torques in spherical joints. We suggest a scheme for computing the friction in two iterative cycles. Practical examples of computing the relative swing of spacecraft stages are given, proving a high convergence rate of the iterations. The results confirm Chetaev's principle of least resistance to motion for mechanical systems with friction constraints.

There are diverse mechanical systems of linked bodies [1-5]. In mechanical engineering, one often deals with systems consisting of a central body (carrier) and several bodies (weights) connected to it. Such systems have a tree structure. The "Soyuz" space launcher vehicle is a widely known example: it has four boosters mounted on the sides of the core vehicle (Fig. 1). In the stage separation process, after the breakup of the lower booster assemblies, the boosters turn by a given angle about the upper booster assemblies; then the upper booster assemblies break up and the boosters are finally jettisoned sideways from the core vehicle. Systems with tree structure also include platform devices and launch simulators, models of spacecraft with fuel tanks, where fuel motion is simulated by oscillations of mathematical pendulums, etc.
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Received 24 September 2003
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