2003/12/11 by C. G. Gray, C G Gray, G. Karl +3
Physics and Astronomy · #Action (physics) #Classical limit #Constraint (computer-aided design) #Limit (mathematics) #Principle of least action #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #Semiclassical physics #Variational principle #physics.class-ph
paper · pdf · doi:10.1088/0034-4885/67/2/r02
arxiv created 2003/12/11 · openalex publication_date 2004/01/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler–Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The reciprocal Maupertuis principle is the classical limit of Schrödinger's variational principle of wave mechanics and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh–Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems. '... the most beautiful and important discovery of Mechanics.' Lagrange to Maupertuis (November 1756)