Interactive Demonstrations Powered by Notebook Technology »
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.
With additional contributions by:
THINGS TO TRY
This Demonstration was inspired by a question in the
"Simulating Mechanics of a Cylinder Rolling on a Parabola".
Lagrangian mechanics can be used to derive the equations of motion .
The potential energy and kinetic energy are repectively
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:
 S. Timoshenko and D. H. Young,
Chapter III, p. 281, Lagrangian Equations for Impulsive Forces.
Sliding on a Parabolic Track
Wolfram Demonstrations Project
Published: November 4, 2013
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Sliding along a Curved Track
Sliding Along a Tautochrone Path
Sliding or Rolling of a Sphere, Cylinder, and Tube down a Semicircular Well
Physics of a Sliding Ladder
Stelios Kapranidis and Reginald Koo
The Sliding Chain Problem
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
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
Browse all topics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
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
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
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.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2018 Wolfram Demonstrations Project & Contributors |
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