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Non-conservative Forces

Non-conservative Forces

Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike conservative forces, non-conservative forces do not have potential energy associated with them. This is because the energy is lost to the system and cannot be turned into useful work later.
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According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of...

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Classical Mechanics

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Updated: May 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Classical mechanics of nonconservative systems.

Chad R Galley¹

¹Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA. crgalley@tapir.caltech.edu

Physical Review Letters

|May 18, 2013

Summary

Hamilton's principle is reformulated for initial value problems, enabling Lagrangian and Hamiltonian dynamics for nonconservative systems. This new approach provides tools to study dissipative effects in classical mechanics and beyond.

Area of Science:

Theoretical Physics
Classical Mechanics
Applied Mathematics

Background:

Hamilton's principle of stationary action is fundamental in physics but has formulation issues.
The principle is a boundary value problem, yet applied to initial value problems, causing subtle errors.

Purpose of the Study:

To present a formulation of Hamilton's principle compatible with initial value problems.
To develop a natural framework for Lagrangian and Hamiltonian dynamics of nonconservative systems.
To provide new tools for studying dissipative effects.

Main Methods:

Reformulation of Hamilton's principle for initial value problems.
Development of generalized Lagrangian and Hamiltonian dynamics for nonconservative systems.
Application of the new formalism to dissipative systems.

Related Experiment Videos

Last Updated: May 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Main Results:

A novel formulation of Hamilton's principle that resolves the initial value problem conflict.
A unified framework for both conservative and nonconservative classical mechanics.
Demonstration of the formalism with viscous drag and dissipative harmonic oscillator examples.

Conclusions:

The new formulation bridges the gap between Hamilton's principle and initial value problem applications.
This work offers new analytical tools for dissipative systems, with potential interdisciplinary applications.
The study advances classical mechanics by naturally incorporating nonconservative dynamics.