Synopsis: Keeping Track of Nonconservative Forces

A modified form of Lagrange’s equations of motion will make it easier to account for energy loss in a mechanical system.
Synopsis figure
NASA

Students learning classical mechanics cut their teeth on some rather artificial sounding problems, like pendulums swinging in vacuum or a bead sliding down a frictionless metal hoop. But in “real-world” calculations, dissipation that comes from nonconservative forces, such as friction, can’t be ignored. In Physical Review Letters, Chad Galley of the California Institute of Technology in Pasadena reports a new way to account for dissipation in the Lagrange equations of motion, a capability that was previously possible only for limited types of forces.

The widely used Lagrange equations can be derived from Hamilton’s principle, which says that a moving particle will follow the trajectory that minimizes the difference between its kinetic and potential energy, called the path of least action. The equations predict the same path for an object under a force as that found with Newton’s laws, but are often easier to solve because they depend on the energy of a system, rather than the vector forces acting upon it. Although ubiquitous in physics, the principle has a well-known limitation: it can’t account for the irreversible effects of energy loss. Galley found a way to modify the principle with a term that captures the energy entering or leaving the system. He has already used the formalism to determine the reaction force on two inspiraling massive bodies (like neutron stars or black holes) that comes from the emission of gravity waves (Physical Review D). The same approach could be applied to finding the motion of an object in a viscous medium or the energy dissipated by a quantum system. – Jessica Thomas


Features

More Features »

Announcements

More Announcements »

Subject Areas

GravitationMechanics

Previous Synopsis

Next Synopsis

Biological Physics

Wind-up DNA

Read More »

Related Articles

Synopsis: Turning up the Ringdown
Astrophysics

Synopsis: Turning up the Ringdown

Stacking up gravitational-wave “ringdown” signals from a set of black hole mergers increases the sensitivity of the signals to black hole properties. Read More »

Focus: Hard and Soft Bounces Explain Asteroid’s Surface Structure
Astrophysics

Focus: Hard and Soft Bounces Explain Asteroid’s Surface Structure

Experiments and computer simulations show that the segregation of small and large rocks on an asteroid’s surface can arise from the way particles hitting the surface collide with the rocks already present. Read More »

Focus: Light Pushes and Pulls
Mechanics

Focus: Light Pushes and Pulls

Two forces coming from a light beam—one based on momentum transfer, the other on thermal effects—drive a tiny gold plate to move in opposite directions. Read More »

More Articles