Bush Master
User ID: 74824125 United States 04/12/2020 03:04 AM Report Abusive Post Report Copyright Violation |
Quoting: Anonymous Coward 76848335 You've got to be crazy Damn the torpedoes! Full speed ahead! Oh,and screw tepco & the V.A. :captain: Thread: GLP-Jukebox |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:04 AM Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 76848335 Sweden 04/12/2020 03:05 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:05 AM Report Abusive Post Report Copyright Violation | |
Bush Master
User ID: 74824125 United States 04/12/2020 03:05 AM Report Abusive Post Report Copyright Violation | Good choice friend Damn the torpedoes! Full speed ahead! Oh,and screw tepco & the V.A. :captain: Thread: GLP-Jukebox |
Anonymous Coward User ID: 78653277 United States 04/12/2020 03:06 AM Report Abusive Post Report Copyright Violation | |
Pooch
User ID: 68879988 Canada 04/12/2020 03:07 AM
Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:08 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:10 AM Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 76848335 Sweden 04/12/2020 03:10 AM Report Abusive Post Report Copyright Violation | The Jerker: Jerk systems In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form
{\displaystyle J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0}J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0 are sometimes called Jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems.[48]
A jerk system's behavior is described by a jerk equation, and for certain jerk equations, simple electronic circuits can model solutions. These circuits are known as jerk circuits.
One of the most interesting properties of jerk circuits is the possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor and the Rössler map, are conventionally described as a system of three first-order differential equations that can combine into a single (although rather complicated) jerk equation. Nonlinear jerk systems are in a sense minimally complex systems to show chaotic behaviour; there is no chaotic system involving only two first-order, ordinary differential equations (the system resulting in an equation of second order only).
An example of a jerk equation with nonlinearity in the magnitude of {\displaystyle x}x is:
{\displaystyle {\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0.}{\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0. Here, A is an adjustable parameter. This equation has a chaotic solution for A=3/5 and can be implemented with the following jerk circuit; the required nonlinearity is brought about by the two diodes:
JerkCircuit01.png In the above circuit, all resistors are of equal value, except {\displaystyle R_{A}=R/A=5R/3}R_{A}=R/A=5R/3, and all capacitors are of equal size. The dominant frequency is {\displaystyle 1/2\pi RC}1/2\pi RC. The output of op amp 0 will correspond to the x variable, the output of 1 corresponds to the first derivative of x and the output of 2 corresponds to the second derivative.
Similar circuits only require one diode[49] or no diodes at all.[50]
See also the well-known Chua's circuit, one basis for chaotic true random number generators.[51] The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system.
|
Bush Master
User ID: 74824125 United States 04/12/2020 03:10 AM Report Abusive Post Report Copyright Violation | I love you! !!!! SOD! Damn the torpedoes! Full speed ahead! Oh,and screw tepco & the V.A. :captain: Thread: GLP-Jukebox |
Pooch
User ID: 68879988 Canada 04/12/2020 03:11 AM
Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 76848335 Sweden 04/12/2020 03:12 AM Report Abusive Post Report Copyright Violation | The Jerker: Jerk systems In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form
{\displaystyle J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0}J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0 are sometimes called Jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems.[48]
A jerk system's behavior is described by a jerk equation, and for certain jerk equations, simple electronic circuits can model solutions. These circuits are known as jerk circuits.
One of the most interesting properties of jerk circuits is the possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor and the Rössler map, are conventionally described as a system of three first-order differential equations that can combine into a single (although rather complicated) jerk equation. Nonlinear jerk systems are in a sense minimally complex systems to show chaotic behaviour; there is no chaotic system involving only two first-order, ordinary differential equations (the system resulting in an equation of second order only).
An example of a jerk equation with nonlinearity in the magnitude of {\displaystyle x}x is:
{\displaystyle {\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0.}{\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0. Here, A is an adjustable parameter. This equation has a chaotic solution for A=3/5 and can be implemented with the following jerk circuit; the required nonlinearity is brought about by the two diodes:
JerkCircuit01.png In the above circuit, all resistors are of equal value, except {\displaystyle R_{A}=R/A=5R/3}R_{A}=R/A=5R/3, and all capacitors are of equal size. The dominant frequency is {\displaystyle 1/2\pi RC}1/2\pi RC. The output of op amp 0 will correspond to the x variable, the output of 1 corresponds to the first derivative of x and the output of 2 corresponds to the second derivative.
Similar circuits only require one diode[49] or no diodes at all.[50]
See also the well-known Chua's circuit, one basis for chaotic true random number generators.[51] The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system.
Quoting: Anonymous Coward 76848335 |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:12 AM Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 78653277 United States 04/12/2020 03:12 AM Report Abusive Post Report Copyright Violation | |
Bush Master
User ID: 74824125 United States 04/12/2020 03:13 AM Report Abusive Post Report Copyright Violation | Ftw Damn the torpedoes! Full speed ahead! Oh,and screw tepco & the V.A. :captain: Thread: GLP-Jukebox |
Pooch
User ID: 68879988 Canada 04/12/2020 03:14 AM
Report Abusive Post Report Copyright Violation | The Jerker: Jerk systems In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form
{\displaystyle J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0}J\left({\overset {...}{x}},{\ddot {x}},{\dot {x}},x\right)=0 are sometimes called Jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems.[48]
A jerk system's behavior is described by a jerk equation, and for certain jerk equations, simple electronic circuits can model solutions. These circuits are known as jerk circuits.
One of the most interesting properties of jerk circuits is the possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor and the Rössler map, are conventionally described as a system of three first-order differential equations that can combine into a single (although rather complicated) jerk equation. Nonlinear jerk systems are in a sense minimally complex systems to show chaotic behaviour; there is no chaotic system involving only two first-order, ordinary differential equations (the system resulting in an equation of second order only).
An example of a jerk equation with nonlinearity in the magnitude of {\displaystyle x}x is:
{\displaystyle {\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0.}{\frac {\mathrm {d} ^{3}x}{\mathrm {d} t^{3}}}+A{\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+{\frac {\mathrm {d} x}{\mathrm {d} t}}-|x|+1=0. Here, A is an adjustable parameter. This equation has a chaotic solution for A=3/5 and can be implemented with the following jerk circuit; the required nonlinearity is brought about by the two diodes:
JerkCircuit01.png In the above circuit, all resistors are of equal value, except {\displaystyle R_{A}=R/A=5R/3}R_{A}=R/A=5R/3, and all capacitors are of equal size. The dominant frequency is {\displaystyle 1/2\pi RC}1/2\pi RC. The output of op amp 0 will correspond to the x variable, the output of 1 corresponds to the first derivative of x and the output of 2 corresponds to the second derivative.
Similar circuits only require one diode[49] or no diodes at all.[50]
See also the well-known Chua's circuit, one basis for chaotic true random number generators.[51] The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system.
Quoting: Anonymous Coward 76848335 |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:14 AM Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 78653277 United States 04/12/2020 03:15 AM Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 76848335 Sweden 04/12/2020 03:15 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:16 AM Report Abusive Post Report Copyright Violation | |
Swearbox
User ID: 77978222 Canada 04/12/2020 03:17 AM
Report Abusive Post Report Copyright Violation | Chill out, its just a Lancashire Rose |
Pooch
User ID: 68879988 Canada 04/12/2020 03:17 AM
Report Abusive Post Report Copyright Violation | |
Bush Master
User ID: 74824125 United States 04/12/2020 03:17 AM Report Abusive Post Report Copyright Violation | Damn the torpedoes! Full speed ahead! Oh,and screw tepco & the V.A. :captain: Thread: GLP-Jukebox |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:17 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:19 AM Report Abusive Post Report Copyright Violation | |
Pooch
User ID: 68879988 Canada 04/12/2020 03:19 AM
Report Abusive Post Report Copyright Violation | |
Anonymous Coward User ID: 76848335 Sweden 04/12/2020 03:20 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:20 AM Report Abusive Post Report Copyright Violation | |
Kevin's Handler
User ID: 76316261 United States 04/12/2020 03:22 AM Report Abusive Post Report Copyright Violation | |