11043
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Damped Spherical Spring Pendulum
A damped spherical spring pendulum consists of a bob suspended by a spring from a fixed pivot. This Demonstration traces the path of the bob.
This system has the following three degrees of freedom: the length of the spring
and the spherical coordinates of the center of the bob,
and
.
The three equations of motion are:
,
,
,
where
is the mass of the bob and
is the damping coefficient of the system.
Among the many chaotic tracks, the phase curves show many interesting periodic orbits, obtained by changing the parameters of the system.
Contributed by:
Erik Mahieu
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Automatic Animation
SNAPSHOTS
DETAILS
The equations of motion are similar to those of the damped spherical pendulum with one additional degree of freedom,
, and one more equation:
.
This equation expresses the longitudinal acceleration of the spring, which consists of four parts:
• gravity,
• spring elasticity,
• radial centrifugal force,
• tangential centrifugal force,
RELATED LINKS
Spherical Coordinates
(
Wolfram
MathWorld
)
Degree of Freedom
(
Wolfram
MathWorld
)
Spherical Pendulum
(
Wolfram Demonstrations Project
)
Damped Spherical Pendulum
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Erik Mahieu
"
Damped Spherical Spring Pendulum
"
http://demonstrations.wolfram.com/DampedSphericalSpringPendulum/
Wolfram Demonstrations Project
Published: October 19, 2011
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
Rigid Body Pendulum on a Flywheel
Nasser M. Abbasi
Pendulum Dangling from a Spring
Erik Mahieu
Spring-Cart-Pendulum System
Erik Mahieu
Varying Period of a Damped Pendulum
Erik Mahieu
Crankshaft-Driven Pendulum
Erik Mahieu
Bouncing Bob Pendulum
Erik Mahieu
Spring Pendulum
Michael Trott
Damped Swing Pendulum
Balázs Kiss (Budapest University of Technology and Economics)
The Damped Nonlinear Pendulum
Enrique Zeleny
Dynamics of a Spring-Pendulum System
Erik Mahieu
Related Topics
3D Graphics
Dynamical Systems Theory
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+