Classical Physics


A Harmonic Oscillator in a Potential Energy Proportional to the Square of the Second Derivative of the Coordinate with Respect to Time

Authors: Faisal Amin Yassein Abdelmohssin

In search to construct a Lagrangian functional of a damped harmonic oscillator I thought to study higher derivatives of coordinates with respect to time in the Lagrangian of a simple harmonic oscillator by adding a term proportional to the square of the second derivative of the coordinate with respect to time in its Lagrangian. In Newtonian mechanics a damping term is added directly to the equation of motion of a simple harmonic oscillator, whereas in Lagrangian and Hamiltonian mechanics (Analytical Mechanics as opposed to Vectroial Mechanics of Newton) adding a term to the Lagrangian of the simple harmonic oscillator wouldn’t reveal whether the term is a damping driving or a forced driving agent until one study the solutions of the equation of motion. Here, The Euler-Lagrange and equation of motion of a harmonic oscillator in a potential energy proportional to the square of the second derivative of the coordinate with respect to time have been formulated and discussed. The equation of motion is derived from Euler-Lagrange equation by performing the partial derivatives on the Lagrangian functional of the second variation of the calculus of variations.

Comments: 12 Pages.

Download: PDF

Submission history

[v1] 2017-09-17 06:15:04

Unique-IP document downloads: 23 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus