Summary of Hamilton-Jacobi mechanics

Thread starter vanesch
Start date Nov 30, 2006
Tags

Mechanics

AI Thread Summary

The discussion focuses on a summary of Hamilton-Jacobi mechanics, drawing inspiration from Goldstein's work on Lagrangian and Hamiltonian formulations of classical mechanics. The author presents the content in an informal style, aiming to make it accessible and useful for readers. There is a suggestion to enhance the summary by including a derivation of the Euler-Lagrange equations based on the principle of least action. This addition could provide a more comprehensive understanding of the topic. The overall goal is to clarify and enrich the discussion around Hamilton-Jacobi mechanics.

Nov 30, 2006

vanesch

Staff Emeritus

Science Advisor

Gold Member

Some while ago I wrote this short summary, inspired by Goldstein, about Lagrangian and Hamiltonian's formulations of classical mechanics, in a rather informal style. Maybe it can be useful to some people.

Physics news on Phys.org

Aug 18, 2007

quetzalcoatl9

this is good, maybe a derivation of the euler-lagrange equations right from the start (via least action) would be something to add to it

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...

View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

View full post »