• Corpus ID: 248965140

When action is not least for systems with action-dependent Lagrangians

  title={When action is not least for systems with action-dependent Lagrangians},
  author={Joseph Ryan},
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… 

Figures and Tables from this paper


The Extrema of an Action Principle for Dissipative Mechanical Systems
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the
An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a
Classical mechanics of nonconservative systems.
A formulation of Hamilton's principle that is compatible with initial value problems is presented, which leads to a natural formulation for the Lagrangian and Hamiltonian dynamics of generic nonconservative systems, thereby filling a long-standing gap in classical mechanics.
When action is not least
We examine the nature of the stationary character of the Hamilton action S for a space-time trajectory (worldline) x(t) of a single particle moving in one dimension with a general time-dependent
A generalization of the Lagrange–Hamilton formalism with application to non-conservative systems and the quantum to classical transition
This work has two aims. The first is to develop a Lagrange–Hamilton framework for the analysis of multi-degree-of-freedom nonlinear systems in which non-conservative effects are included in the
Is it possible to formulate least action principle for dissipative systems
A longstanding open question in classical mechanics is to formulate the least action principle for dissipative systems. In this work, we give a general formulation of this principle by considering a
Some Further Remarks on Hamilton’s Principle
The development of the equations of motion for a mechanical ystem from Hamilton’s principle can be viewed as a problem in he calculus of variations when the constraints on the system are olonomic and