Birkhoff’s Equations

Abstract

As is well-known, the study of Newtonian systems in first-order form permits the achievement of a remarkable symbiosis among analytic techniques (e.g., canonical formulations of variational principles), algebraic techniques (e.g., theory of Lie algebras), and geometric techniques (e.g., the symplectic and contact geometries). The availability of these powerful mathematical tools then renders the study important for several aspects of mechanics, ranging from practical applications (e.g., treatment of systems via the Hamilton-Jacobi theory) to formal problems (e.g., coordinate-free globalizations).