This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
This shows the motion of a mass suspended from a spring, with damping. An accurate solution requires a small time step and RK4 as the integration algorithm. (simplified clone)
 FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION     BEWARE pushing increased growth blows the system!    (governments are trying to push growth on already unstable systems !)  The existing global capitalistic growth paradigm is totally flawed  The chaotic turbulence is the result of th
FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION 
 BEWARE pushing increased growth blows the system!
(governments are trying to push growth on already unstable systems !)

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept and flawed strategy of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)

Thanks to  https://insightmaker.com/insight/1830/Rossler-Chaotic-Attractor for this example of chaos, and the  transition  to chaos. "After running the default settings Bossel describes A=0.2, B=0.2, Initial Values X=0 Y=2 and Z=0 and varying C=2,3,4,5 shows period doubling and transition to chaotic
Thanks to
https://insightmaker.com/insight/1830/Rossler-Chaotic-Attractor
for this example of chaos, and the transition to chaos. "After running the default settings Bossel describes A=0.2, B=0.2, Initial Values X=0 Y=2 and Z=0 and varying C=2,3,4,5 shows period doubling and transition to chaotic behavior."

We're looking into environmental applications in our course, and how dramatically dynamics can change, based on a small change in parameters. Climate change "suffers" this chaotic behavior, we fear, and we're going to be "taken by surprise" when the dynamics changes on us suddenly....

Andy Long
 Perceptual Control Theory Model of Balancing an Inverted Pendulum. See  Kennaway's slides  on Robotics. as well as PCT example WIP notes. Compare with  IM-1831  from Z209 from Hartmut Bossel's System Zoo 1 p112-118

Perceptual Control Theory Model of Balancing an Inverted Pendulum. See Kennaway's slides on Robotics. as well as PCT example WIP notes. Compare with IM-1831 from Z209 from Hartmut Bossel's System Zoo 1 p112-118

In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) ​variiert auch die Chaotizität des System. Zusätzlich wird al
In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) ​variiert auch die Chaotizität des System.
Zusätzlich wird als Gedankenexperiment die Reibungskraft die durch ein hypothetisches umgebenes Medium entsteht eingeführt und die Auswirkung auf die Chaotizität gezeigt.
 
  Um ponto
material percorre uma trajetória circular de raio R = 20m com movimento uniformemente variado e
aceleração escalar a = 5m/s². Sabendo-se que no instante
t = 0 sua velocidade escalar é nula, determine no instante t = 2s os módulos da:   a) Velocidade vetorial;  b) Aceleração tangencial;

Um ponto material percorre uma trajetória circular de raio R = 20m com movimento uniformemente variado e aceleração escalar a = 5m/s². Sabendo-se que no instante t = 0 sua velocidade escalar é nula, determine no instante t = 2s os módulos da:

a) Velocidade vetorial;

b) Aceleração tangencial;

c) Aceleração centrípeta;

d) Aceleração vetorial.

Fonte: (RAMALHO,NICOLAU E TOLEDO; Fundamentos da Física, Volume 1, 8ª edição, pp. 12 – 169, 2003).

Clique aqui para ver uma descrição do que é Movimento Vertical no Vácuo.

Simulation der Umlaufbahn der Erde um die Sonne
Simulation der Umlaufbahn der Erde um die Sonne
 Dieses Modell beschreibt die Dynamik des Wasserlösens. Siehe dazu das Video "Harnflussmessung"  https://youtu.be/EgOaPAEmXo0
Dieses Modell beschreibt die Dynamik des Wasserlösens. Siehe dazu das Video "Harnflussmessung"
https://youtu.be/EgOaPAEmXo0
  object is projected with an initial velocity u at an angle to the horizontal direction.  We assume that there is no air resistance .Also since the body first goes up and then comes down after reaching the highest point , we will use the Cartesian convention for signs of different physical quantiti

object is projected with an initial velocity u at an angle to the horizontal direction.

We assume that there is no air resistance .Also since the body first goes up and then comes down after reaching the highest point , we will use the Cartesian convention for signs of different physical quantities. The acceleration due to gravity 'g' will be negative as it acts downwards.

h=v_ox*t-g*t^2/2

l=v_oy*t
An steel cylinder oscillates inside a glass tube and over confined air within a glass bottle. As consecuence one observes an oscilation of the inside presure and the inner energy (temperature).
An steel cylinder oscillates inside a glass tube and over confined air within a glass bottle. As consecuence one observes an oscilation of the inside presure and the inner energy (temperature).
 
  Um corpo é
lançado obliquamente no vácuo com velocidade inicial de 100 m/s, numa direção que forma com
a horizontal um ângulo x, tal que sen(x) = 0,8 e cos(x) = 0,6. Adotando g = 10m/s², determine:   a) Os módulos das componentes horizontal e vertical da
velocidade no instante de lançamento;  b)

Um corpo é lançado obliquamente no vácuo com velocidade inicial de 100 m/s, numa direção que forma com a horizontal um ângulo x, tal que sen(x) = 0,8 e cos(x) = 0,6. Adotando g = 10m/s², determine:

a) Os módulos das componentes horizontal e vertical da velocidade no instante de lançamento;

b) O instante em que o corpo atinge o ponto mais alto da trajetória;

c) A altura máxima atingida pelo corpo;

d) O alcance do lançamento.

Fonte: (RAMALHO, NICOLAU E TOLEDO;Fundamentos da Física, Volume 1, 8ª edição, pp. 12 – 169, 2003).

Clique aqui para ver uma descrição do que é Lançamento Oblíquo no vácuo.

In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simmuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) ​variiert auch die Chaotizität des System. Zusätzlich wir al
In diesem Modell wird das Verhalten, also die Positionsänderungen von drei Körpern innerhalb eines Bezugssystems aufgrund der Gravitationskraft simmuliert. Je nach Änderung der Parameter (Masse, Ausgangsposition, Radius der Massen(-punkte) ​variiert auch die Chaotizität des System.
Zusätzlich wir als Gedankenexperiment die Reibungskraft die durch ein hypothetisches umgebenes Medium entsteht eingeführt und die Auswirkung auf die Chaotizität gezeigt.
A simple model of a capacitor being charged. The instantaneous charge grows at a rate equal to the difference between it and the final charge, given as CV, divided by a time constant, which can set with a slider.
A simple model of a capacitor being charged. The instantaneous charge grows at a rate equal to the difference between it and the final charge, given as CV, divided by a time constant, which can set with a slider.
 
  Uma roda-gigante
de raio 14 m gira em torno de um eixo horizontal. Um passageiro sentado em uma
cadeira, move-se com velocidade linear v=7 m/s. Determine:   a) A velocidade angular do
movimento.  b) O módulo da aceleração centrípeta do passageiro.  c) Em quanto tempo o
passageiro executa uma vol

Uma roda-gigante de raio 14 m gira em torno de um eixo horizontal. Um passageiro sentado em uma cadeira, move-se com velocidade linear v=7 m/s. Determine:

a) A velocidade angular do movimento.

b) O módulo da aceleração centrípeta do passageiro.

c) Em quanto tempo o passageiro executa uma volta completa.

Clique aqui para ver uma descrição do que é Movimento Circular.

Filling a tank with a pump. Tank is straight-walled (constant capacitance). Flow is laminar (linear flow relation.    Energy quantities have been added.
Filling a tank with a pump. Tank is straight-walled (constant capacitance). Flow is laminar (linear flow relation.

Energy quantities have been added.
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency.     The oscillator is driven with a force that is a sine function o
This shows the motion of a driven damped harmonic oscillator, described in terms of the undamped natural frequency, and a frequency gamma that reflects the degree of damping, parameterized as a damping ratio gamma/natural frequency. 

The oscillator is driven with a force that is a sine function of time, with a frequency that can be varied, expressed as a forcing ratio driving frequency/natural frequency.

An accurate solution requires a small time step and RK4 as the integration algorithm.
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION  The existing global capitalistic growth paradigm is totally flawed  Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a compon
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

Cette simulation est une version optimisée de l'eaurdinateur, dans laquelle on a utilisé l'influence d'un flux sur un autre pour économiser les réservoirs utilisés pour diviser par deux les flux de sortie des portes AND.   Nous n'avons malheureusement pas réussi à changer la couleur de l'état en fon
Cette simulation est une version optimisée de l'eaurdinateur, dans laquelle on a utilisé l'influence d'un flux sur un autre pour économiser les réservoirs utilisés pour diviser par deux les flux de sortie des portes AND.

Nous n'avons malheureusement pas réussi à changer la couleur de l'état en fonction de sa valeur. Celle-ci peut être changée dans le panneau de configuration, afin de tester des valeurs différentes.

On notera que pour obtenir un résultat correct, deux conditions sont nécessaires:
1°) Il faut attendre que les flux dans les portes se stabilisent, ce qui prend pas moins de 10 secondes (et qui reflète le délai de latence inhérent à tout circuit, qui correspond environ au nombre maximum de portes logiques traversées entre l'entrée et la sortie du circuit.
2°) Il faut utiliser la méthode de simulation basée sur une approximation de Runge-Kutta, sous peine de voir apparaître des oscillations parasites dans certaines portes qui rendent le résultat instable.


  ​S-Curve + Delay for Bell Curve Showing Erlang Distribution      Generation of Bell Curve from Initial Market through Delay in Pickup of Customers     This provides the beginning of an Erlang distribution model      The  Erlang distribution  is a two parameter family of continuous  probability dis
​S-Curve + Delay for Bell Curve Showing Erlang Distribution

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

  • a positive integer 'shape' 
  • a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.