Classical Mechanics of Nonconservative Systems

2012/10/09 by Chad R. Galley · 2 voices · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum chaos and dynamical systems #gr-qc #math-ph #math.OC #physics.flu-dyn #physics.plasm-ph

paper · pdf · doi:10.1103/physrevlett.110.174301

openalex publication_date 2013/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics. Thus, dissipative effects, for example, can be studied with new tools that may have applications in a variety of disciplines. The new formalism is demonstrated by two examples of nonconservative systems: an object moving in a fluid with viscous drag forces and a harmonic oscillator coupled to a dissipative environment.

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Discussions

• Yes, there is the classical Schwinger/Keldysh "in-in" variational principle where there are only initial "in" conditions and no final "out" conditions on the physical path. This even works for dissipa [stackexchange, 5 points]
• I'm trying to work through Galley's paper, The classical mechanics of non-conservative systems . It starts with a toy problem to demonstrate the need for his full approach. I'm certain understanding t [stackexchange, 1 points]

Related

• The principle of stationary nonconservative action for classical mechanics and field theories
• Classical Lagrange formalism for non-conservative dynamical systems
• Hamiltonian treatment of non-conservative systems
• Extended Hamilton's principle
• A Sort of Relation among a Dissipative Mechanical System and Conservative Ones