Geometrical approach to the swinging pendulum dynamics

This paper shows how geometrical tools can describe a two degrees-of-freedom mechanical system (a swinging pendulum). First a brief introduction to the subject of geometrodynamics is given and then the fundamental quantities of the technique are found. Next the Jacobi–Levi–Civita equation is explicitely obtained and transformed to a scalar differential equation that is numerically solved. Qualification of regular and chaotic dynamics of our investigated system is illustrated and discussed.