From physical principles to classical Hamiltonian mechanics

TL;DR

This paper derives the Hamiltonian formulation of classical mechanics directly from fundamental principles, emphasizing the role of state labels and conservation laws without relying on Lagrangian mechanics.

Contribution

It introduces a direct derivation of Hamiltonian mechanics based on state labels and conservation, bypassing the traditional Lagrangian approach.

Findings

Hamilton's equations are derived from label conservation principles.

The approach emphasizes deterministic and reversible processes.

Provides a foundational perspective on classical mechanics.

Abstract

We derive the Hamiltonian formulation of classical mechanics directly, without reference to Lagrangian mechanics. We start from the definition of states in terms of labels used to identify them, and show how, under a deterministic and reversible process, the conservation of the cardinality of the labels leads to Hamilton's equations.