Media Summary: This is the exact same simulation as the previous double and, of course, things can be taken to an unsightly extreme when it comes to building chaotic compound pendula. Spherical pendula, like planar pendula, exhibit chaotic dynamics when coupled together. This double

Appdynsys Spherical Pendulum Initial Conditions - Detailed Analysis & Overview

This is the exact same simulation as the previous double and, of course, things can be taken to an unsightly extreme when it comes to building chaotic compound pendula. Spherical pendula, like planar pendula, exhibit chaotic dynamics when coupled together. This double What is chaotic dynamics? One of the hallmarks of chaos is something called SDIC = sensitive dependence on let's see what happens when we simulate a you can build (or find for sale) pendular configurations built from objects other than rigid rods. this one, made from solid rings, ...

Let's repeat the simulation of the (chaotic!) double Let's take a look at that same simulation of a double Here we use the equations of motion we derived for theta and phi from the last video to simulate the This is part of a series of short simulations without audio on applied dynamical systems...) We've seen that an inverted

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AppDynSys : Spherical Pendulum : Initial Conditions
AppDynSys : Spherical Pendulum : Spin Around
AppDynSys : Spherical Pendulum : Double Bottom View
AppDynSys : Pendumonium : Stranger Things
AppDynSys : Spherical Pendulum : Double
AppDynSys : Double pendulum : SDIC
AppDynSys : Pendumonium : Septuple Pendulum!
AppDynSys : Pendumonium : Triple Pendulum
AppDynSys : Pendumonium : Strange Rings
AppDynSys : Universal Joint : Double Pendulum
AppDynSys : Universal Joint : Double Pendulum Bottom
AppDynSys : Phase Space : Undamped Pendulum
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AppDynSys : Spherical Pendulum : Initial Conditions

AppDynSys : Spherical Pendulum : Initial Conditions

If we change the type of joint on a

AppDynSys : Spherical Pendulum : Spin Around

AppDynSys : Spherical Pendulum : Spin Around

The previous simulation of a

AppDynSys : Spherical Pendulum : Double Bottom View

AppDynSys : Spherical Pendulum : Double Bottom View

This is the exact same simulation as the previous double

AppDynSys : Pendumonium : Stranger Things

AppDynSys : Pendumonium : Stranger Things

and, of course, things can be taken to an unsightly extreme when it comes to building chaotic compound pendula.

AppDynSys : Spherical Pendulum : Double

AppDynSys : Spherical Pendulum : Double

Spherical pendula, like planar pendula, exhibit chaotic dynamics when coupled together. This double

AppDynSys : Double pendulum : SDIC

AppDynSys : Double pendulum : SDIC

What is chaotic dynamics? One of the hallmarks of chaos is something called SDIC = sensitive dependence on

AppDynSys : Pendumonium : Septuple Pendulum!

AppDynSys : Pendumonium : Septuple Pendulum!

let's see what happens when we simulate a

AppDynSys : Pendumonium : Triple Pendulum

AppDynSys : Pendumonium : Triple Pendulum

why stop with a double

AppDynSys : Pendumonium : Strange Rings

AppDynSys : Pendumonium : Strange Rings

you can build (or find for sale) pendular configurations built from objects other than rigid rods. this one, made from solid rings, ...

AppDynSys : Universal Joint : Double Pendulum

AppDynSys : Universal Joint : Double Pendulum

Let's repeat the simulation of the (chaotic!) double

AppDynSys : Universal Joint : Double Pendulum Bottom

AppDynSys : Universal Joint : Double Pendulum Bottom

Let's take a look at that same simulation of a double

AppDynSys : Phase Space : Undamped Pendulum

AppDynSys : Phase Space : Undamped Pendulum

An undamped

Simulating the Spherical Pendulum with Mathematica

Simulating the Spherical Pendulum with Mathematica

Here we use the equations of motion we derived for theta and phi from the last video to simulate the

AppDynSys : Double Pendulum : Chaos

AppDynSys : Double Pendulum : Chaos

What happens if, instead of shaking a

AppDynSys : 2nd Order ODEs : Pendulum

AppDynSys : 2nd Order ODEs : Pendulum

A simple

AppDynSys : Pendula : Inverted, Shaken, & Stabilized

AppDynSys : Pendula : Inverted, Shaken, & Stabilized

This is part of a series of short simulations without audio on applied dynamical systems...) We've seen that an inverted

Motion of a Spherical Pendulum(H=1.1, L=1.59)

Motion of a Spherical Pendulum(H=1.1, L=1.59)

http://rasilse222.sakura.ne.jp/math_spherical.html.