بدست آوردن معادلات حركت پاندول فضايي و حل آنها براي شرايط اوليه مختلف

Deriving the Equation of Motion for Space Pendulums and Its Solution for Different Initial Conditions

Here we study the space pendulums, derive their equations of motion and solve them for different initial conditions. Space pendulum is a model for many physical and engineering problems. For example tower cranes while moving a load can be modeled by a space pendulum. In this article the equations of motion for a tower crane are derived using Lagrangian method. Then the numerical solutions (for the general condition) and the analytic solutions (by simplifying assumptions) are presented. Finally the effect of the radial velocity of pendulum on its maximum deviation from equilibrium is studied.