Geodesics on a Pseudosphere: Analytical and Numerical Approaches

Geodesics on a pseudosphere are examined through analytical and numerical approaches. The pseudosphere, a surface of revolution with constant negative curvature, is characterized using the first fundamental form. The geodesic equations are derived via Christoffel symbols and transformed into a first-order Bernoulli equation. Solutions are obtained both analytically and using Python’s LSODA method for numerical integration. Results illustrate the behavior of geodesic trajectories and their dependence on initial conditions. The study provides insights into differential geometry and mathematical physics, highlighting the significance of geodesics in negatively curved spaces.