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

@inproceedings{Ryan2022WhenAI, title={When action is not least for systems with action-dependent Lagrangians}, author={Joseph Ryan}, year={2022} }

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…

## References

SHOWING 1-10 OF 55 REFERENCES

The Extrema of an Action Principle for Dissipative Mechanical Systems

- Mathematics
- 2014

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

- Mathematics
- 2018

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.

- PhysicsPhysical review letters
- 2013

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

- Mathematics
- 2007

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

- Physics
- 2021

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

- Physics
- 2012

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

- Mathematics
- 2011

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…