Extended Hamilton’s principle applied to geometrically exact Kirchhoff sliding rods

This article addresses the dynamic modeling of geometrically exact sliding Cosserat rods. Such systems need to consider non-material time-varying domains which Lagrangian view point solid mechanics is inappropriate. In here presented, we use model inextensible Kirchhoff rods along a domain whose time variations are not necessarily imposed but governed by dynamics, i.e. depend on configuration rod. To progress through derivation, variational calculus Lie group introduced Poincaré, and apply it an extension Hamilton’s principle holding for open rod systems, derived in article. extended uses moving tube across material slides. The resulting closed formulation dynamics takes form set Cosserat–Poincaré’s partial differential equations governing time-evolution cross-section pause tube, coupled with ordinary Lagrange’s equation motion tube. While emphasize formulations, approach numerically illustrated few examples related so called spaghetti problem.