11166
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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.
Contributed by:
Erik Mahieu
With additional contributions by:
Franz Brandhuber
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
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:
,
,
.
Reference
[1] S. Timoshenko and D. H. Young,
Advanced Dynamics
Chapter III, p. 281, Lagrangian Equations for Impulsive Forces.
PERMANENT CITATION
Erik Mahieu
"
Sliding on a Parabolic Track
"
http://demonstrations.wolfram.com/SlidingOnAParabolicTrack/
Wolfram Demonstrations Project
Published: November 4, 2013
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 »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Sliding along a Curved Track
Erik Mahieu
Sliding Along a Tautochrone Path
Erik Mahieu
Sliding or Rolling of a Sphere, Cylinder, and Tube down a Semicircular Well
Erik Mahieu
Physics of a Sliding Ladder
Stelios Kapranidis and Reginald Koo
The Sliding Chain Problem
Clay Gruesbeck
Sliding Block Displacing a Wedge
Sandeep R. Murthy
A Sliding Element in Rheological Models
Mark D. Normand and Micha Peleg
A Rod Sliding in a Semicircular Well
Sarah Lichtblau
Parabolic Projectile Motion: Shooting a Harmless Tranquilizer Dart at a Falling Monkey
Roberto Castilla-Meléndez, Roxana Ramírez-Herrera, and José Luis Gómez-Muñoz
Disk Sliding or Rolling in a Semicircular Well
Sarah Lichtblau
Related Topics
Mechanics
Browse all topics
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+