Classical Mechanics of Nonconservative Systems
- Creators
- Galley, Chad R.
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.
Additional Information
© 2013 American Physical Society. Received 1 September 2012; published 22 April 2013. I thank Y. Chen, C. Cutler, K. Hawbaker, A. Leibovich, H. Miao, E. Poisson, I. Rothstein, G. Schäfer, L. Stein, A. Tolley, M. Vallisneri, and especially A. Zenginoğlu for discussions and comments of previous drafts. This work was supported in part by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory administered by the Oak Ridge Associated Universities through a contract with NASA.Attached Files
Published - PhysRevLett.110.174301.pdf
Submitted - 1210.2745v1.pdf
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Additional details
- Alternative title
- The classical mechanics of non-conservative systems
- Eprint ID
- 37316
- Resolver ID
- CaltechAUTHORS:20130305-143741720
- NASA Postdoctoral Program
- Created
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2013-03-27Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Caltech groups
- TAPIR