“…We can apply the above‐described mechanical approach in order to find the geodesics for the case of the
‐spheres. Although we can generally find geodesics directly solving the system of second‐order differential equations () obtained from the Lagrangian function () or () with
(see, e.g., Kovalchuk et al
10,11 ), we can also perform the corresponding Legendre transformation to pass from the Lagrangian to Hamiltonian formulation and then obtain the geodesic equations in the form of the first‐order Hamilton's equations (see, e.g., Kovalchuk et al
4,8 ). From the geometrical perspective, these two approaches are equivalent, but from the mechanical one it can be proven that the phase‐space description is more fundamental both in the classical and quantum physics (see, e.g., Sławianowski et al 12 ).…”