Besides Hamiltonian and Lagrangian, are there any other similar functions useful when studying mechanical system? (It is ok if the functions do not work well and lead to mistakes in some situation, but it should be of interest in some period in the history.)

This question is invoked by Is the Legendre transformation a unique choice in analytical mechanics?. I doubt there are some historical reasons why we use Hamiltonian and Lagrangian a lot today.

  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/265248/2451 $\endgroup$
    – Qmechanic
    Jul 20 at 14:10
  • $\begingroup$ @Qmechanic not duplicate, functions here is not supposed to be able to derive or recover the Newtonian theory, besides, functions with problems are ok here, so long as it is of interest in the past. $\endgroup$
    – Michael
    Jul 20 at 15:18