Operational classical mechanics: holonomic systems

We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts will be rediscovered entirely new perspective. start by expressing the basic position and velocity point particles as eigenvalues self-adjoint operators acting on a suitable Hilbert space. The concept Holonomic constraint is shown to equivalent restriction linear subspace free principal we obtain are: (1) Lagrange equations motion are derived use D'Alembert or Hamilton principles, (2) constraining forces obtained multipliers, (3) passage position-velocity position-momentum description movement done Legendre transformation, (4) Koopman-von Neumann theory result our ab initio approach, (5) work Schwinger action principle for systems generalized include holonomic constraints.