Appendixes to the article Optimization of the simultaneous start mode of the derricking and the lifting mechanisms during steady slewing of the jib crane

This repository contains appendices to the article “Optimization of the Simultaneous Start Mode of the Derricking and the Lifting Mechanisms during Steady Slewing of the Jib Crane”.The supplementary material includes detailed mathematical derivations, boundary conditions, penalty functions, analytical expressions, and additional computational results that support the main study. In particular, the appendices contain:- derivation of kinetic and potential energy functions;- penalty functions used to satisfy optimization constraints;- initial and final boundary conditions of the system motion;- derivation of higher-order derivatives for generalized coordinate functions;- determination of polynomial coefficients for motion laws;- convergence analysis of the optimization criterion using the VCT-PSO method.These materials are provided to ensure transparency, reproducibility, and a deeper understanding of the developed optimization model for jib crane motion coordination.