Every wondered what is the Lagrangian? What is the action? What does the action means physically? Whether there is a geometrical interpretation for the action principle? I certainly have for a long time!
In this video I show you what I understood. Full details in the paper https://doi.org/10.1038/s41598-023-39145-y (pre-print at https://arxiv.org/abs/2208.06428 )
Intro (0:00)
Geometrical insight (1:27)
L ≠ T - V (6:19)
Hamiltonian (Det/Rev) flow (8:18)
Action principle explained (15:22)
Conclusion (20:03)