In all known to me textbooks on classical mechanics explaining the Hamiltonian formalism (e.g. Landau-Lifshitz, vol. 1, or “Mathematical methods of classical mechanics” by Arnold) no applications to concrete problems of classical mechanics are given. (However this formalism plays a role later in quantum mechanics to partly motivate the Schroedinger equation.  )

I am looking for a reference (or just a brief description) to applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion.

I am looking for a reference (or just a brief explanation) to applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion.

In all known to me textbooks on classical mechanics explaining the Hamiltonian formalism (e.g. Landau-Lifshitz, vol. 1, or “Mathematical methods of classical mechanics” by Arnold) no applications to concrete problems of classical mechanics are given. (However this formalism plays a role later in quantum mechanics to partly motivate the Schroedinger equation.)

In 1833 Hamilton developed his formalism in classical mechanics.

I am wondering what was his motivation to introduce it? Did he try to solve any concrete problem?

In all known to me modern textbooks on classical mechanics where this formalism is explained (e.g. Landau-Lifshitz, vol. 1, or “Mathematical methods of classical mechanics” by Arnold) no application to concrete problems of classical mechanics is given. This formalism plays a role much later to partly motivate the Schroedinger equation in quantum mechanics.

Are there applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion?

In all known to me textbooks on classical mechanics explaining the Hamiltonian formalism (e.g. Landau-Lifshitz, vol. 1, or “Mathematical methods of classical mechanics” by Arnold) no applications to concrete problems of classical mechanics are given. (However this formalism plays a role later in quantum mechanics to partly motivate the Schroedinger equation. )

I am looking for a reference (or just a brief description) to applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion.