The Generalized Local Instability Criterion from the Geodesic Deviation Equation for Simple Mechanical Systems

The property of sensitive dependence on initial conditions is formulated as the local instability of nearby geodesics. In studying sectional curvature, the bivector formalism is applied. We also show that the trajectories of simple mechanical systems can be put into one-to-one correspondence with geodesics of suitable $N+1$ dimensional space with the Lorentzian signature ($N$ is a dimension of the configuration space). This illustrates the fact that the simple relativistic mechanical systems can be used not only in applications to general relativity and cosmology where the kinetic energy form with the Loretzian signature is indefinite at the very beginning.