Sliding on a Parabolic Track

This Demonstration shows an object sliding with damping on a parabolic track with equation . It explores the effect of the damping coefficient and the parameter on the swing period of the object and the constraining force that keeps it on the track.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


This Demonstration was inspired by a question in the Wolfram Community site, "Simulating Mechanics of a Cylinder Rolling on a Parabola".
Lagrangian mechanics can be used to derive the equations of motion [1].
The potential energy and kinetic energy are repectively
where is the position of the object at time , is the mass of the object, is the Lagrange multiplier, and is the damping coefficient.
This gives the equations of motion:
[1] S. Timoshenko and D. H. Young, Advanced Dynamics Chapter III, p. 281, Lagrangian Equations for Impulsive Forces.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students. »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+