Question

If a given co-ordinate is cyclic in lagrangian, it will also be cyclic in hamiltonian

Answer 1

Joseph-Louis Lagrange(1736–1813)Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomerJoseph-Louis Lagrange in 1788.In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the Lagrange equations of the first kind,[1] which treatconstraints explicitly as extra equations, often using Lagrange multipliers;[2][3] or the Lagrange equations of the second kind, which incorporate the constraints directly by judicious choice ofgeneralized coordinates.[1][4] In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, and time, and contains the information about the dynamics of the system.