More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques

In this article, I demonstrate a new method to derive Jacobi metrics from Randers-Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. I introduce Hamiltonian mechanics with the constraint for relativistic momentum, including a modification for null curves and two applications as exercises: derivation of a relativistic harmonic oscillator, and analysis of Schwarzschild Randers-Finsler metric. Then I describe the main application for constraint mechanics in this article: a new derivation of Jacobi metric for time-like and null curves, comparing the latter with optical metrics. After that, I discuss frame dragging with the Jacobi metric, and two applications for Randers-Finsler metrics: an alternative to Eisenhart lift, and different metrics that share the same Jacobi metric.