Sliding on a Parabolic Track
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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 (November 2013)
With additional contributions by: Franz Brandhuber
Open content licensed under CC BY-NC-SA
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