Affiliation:
1. Department of Physics, Southern Methodist University , Dallas, Texas 75205, USA
Abstract
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action according to the variational principle of Herglotz. This is directly analogous to the variational principle of Hamilton commonly used to derive the dynamics of conservative systems. In a similar fashion, just as the second variation of a conservative system’s action can be used to infer whether that system’s possible trajectories are dynamically stable, so too can the second variation of the action-dependent action be used to infer whether the possible trajectories of non-conservative and dissipative systems are dynamically stable. In this paper, I show, generalizing earlier analyses of the second variation of the action for conservative systems, how to calculate the second variation of the action-dependent action and how to apply it to two physically important systems: a time-independent harmonic oscillator and a time-dependent harmonic oscillator.
Funder
U.S. Department of Energy
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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