Numerical and analytical comparison of the stability and instability of angular motion of a bar drawn by a spring by AGM method

This article's topic is a numerical and analytical comparison of the stability and instability of angular momentum and vibration of a metal bar that is pinned from one side in a place and pulled from the other side with ۲ springs AGM method. We deal with different numerical results related to the stability and instability of the system by changing the parameters of m (mass), L (Length) k (spring constant) for metal rods, and then compare it withAGM and NUM methods. In the steady-state of the bar and spring system and the steady vibration of the bar by increasing the mass of the bar with the fixed values of k and L, the angular momentum (theta) increases with time. The vibration gradually goes out of the steady-state of the system. In this case, the amount of angular momentum (theta) increases by decreasing the spring's value constant when mass and length are constant. In contrast, with increasing the spring's length, the angular momentum decreases, and the system reaches its steady state. In the unstable state in which the bar and spring system have angular acceleration, and the velocity is not constant, the same condition is true, but the angular momentum gradient over time is much greater in this casethan the steady-state of the system, and somehow the system goes out of steady-state.

Keywords:

Angular momentum , Akbari Ganjis method , Dynamic system , Stability , Instability ,