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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
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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
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