Dynamical Trajectories of Simple Mechanical Systems as Geodesics in Space with an Extra Dimension

Dynamical trajectories of simple dynamic

Dynamical trajectories of simple dynamical systems as geodesics—in searching for invariant criteria of chaos in general relativity

✍ Marek Szydłowski 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 359 KB

We will investigate the possibility of describing the chaotic behaviour of trajectories of simple mechanical systems by means of elementary tools of Riemannian differential geometry. From the curvature properties of a Riemannian manifold some relevant consequences about stability (instability) prope