Another Formalism in Classical Mechanics

Dear Colleagues, My name is Lindsay Waterman, a retired academic and former Principal of the Barbados Community College. I am writing to share a new analytical framework I, and my son, Hagos B. Waterman, have developed for classical mechanics: the Watermanian Formalism. This framework operates as a highly efficient alternative separate from Newtonian, Lagrangian, or Hamiltonian dynamics. Key structural and computational advantages of this formalism include: Unified System Handling: Natively models both conservative and non-conservative systems. No External Equations: Resolves dissipative forces without auxiliary identities. Zero Variational Overhead: Operates without "action" principles or variational calculus. Factorization Foundation: Uses direct velocity-space factorization to extract equations. Coordinate Independence: Restricts calculus solely to disentangling entangled coordinates. Multipliers Eliminated: System constraints are absorbed without Lagrange multipliers. I have compiled this framework into a companion pair of papers containing robust, worked solutions for both electrical and mechanical systems. Examples include the damped harmonic oscillator, an electron in a uniform magnetic field, and the Brachistochrone optimization problem. I am eager to share these manuscripts with independent researchers and educators for peer review. If you are willing to review the text and the mathematical proofs, I will gladly upload the PDFs for you. Best regards, Mr. Lindsay A. Waterman