System of first order differential equations fro Lorentz Oscillator.
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override int | NumEquations [get, protected set] |
| Number of first orter differential equations that govern the system. More...
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double | Sigma [get, set] |
| Parameter σ of Lorenz oscillator, the Prandtl number. More...
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double | Ro [get, protected set] |
| Parameter ρ of Lorenz oscillator, the Rayleigh number. More...
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double | Beta [get, set] |
| Parameter β of Lorenz oscillator. More...
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double | InitialX [get, set] |
| Initial Y coordinate of the system. More...
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double | InitialY [get, set] |
| Initial Y coordinate of the system. More...
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double | InitialZ [get, set] |
| Initial Z coordinate of the system. More...
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double | InitialTime [get, set] |
| Initial time. More...
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double | FinalTime [get, set] |
| The final time. More...
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double | Time [get, set] |
| Current time. More...
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double | X [get, set] |
| X coordinate of the current position. More...
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double | Y [get, set] |
| Y coordinate of the current position. More...
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double | Z [get, set] |
| Z coordinate of the current position. More...
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virtual int | NumEquations [get, protected set] |
| Number of equations in the system of first order equations. More...
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int | NumStateVariables [get, set] |
| Number of state variables, including independent variable and function values. More...
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bool | IsHistoryDependent [get, set] |
| Flag indicating whether the problem is history dependent (meaning that it has additional state variables that are not calculated by the solver). More...
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System of first order differential equations fro Lorentz Oscillator.
See http://en.wikipedia.org/wiki/Lorenz_oscillator
$A Igor Jan10 Dec11;
IG.Num.DiffLorenzOscillator.DiffLorenzOscillator |
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double |
sigma, |
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double |
ro, |
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double |
beta |
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) |
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inline |
Construct a system of differential equations for Lorenz oscillator.
- Parameters
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sigma | Parameter σ of Lorenz oscillator, "Prandtl number". |
ro | Parameter ρ of Lorenz oscillator, "Rayleigh number". |
System exhibits chaotic behavior for ρ = 28, but knotted periodic orbits behaviors for other values of ρ. For example, with ρ = 99.96 it becomes a T(3,2) torus knot.
- Parameters
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beta | Parameter β of Lorenz oscillator. |
override void IG.Num.DiffLorenzOscillator.InitializeAndReset |
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inlinevirtual |
Initializes and resets the state of the current problem definition.
All variables are set to initial values.
Any history dependent state variables are reset to the initial state.
Implements IG.Num.DifferentialFirstOrderSystemBase.
override void IG.Num.DiffLorenzOscillator.CalculateFunctionDerivatives |
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double |
t, |
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double[] |
y, |
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double[] |
derivative |
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) |
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inlinevirtual |
Calculates derivatives of searched functions from the current time and form current
- Parameters
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t | Time (independent variable) ad which derivatives are calculated. |
y | Function values (positio and velocity) at the specified time. |
derivative | Array where calculated derivatives of unknown functions (of position and velocity) are stored. |
Implements IG.Num.DifferentialFirstOrderSystemBase.
override void IG.Num.DiffLorenzOscillator.GetInitialFunctionValues |
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double[] |
initialValues | ) |
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inlinevirtual |
Stores initial values of unknown functions (position and velocity) to the specified array.
- Parameters
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initialValues | Array where initial funtion values are stored. |
Implements IG.Num.DifferentialFirstOrderSystemBase.
override double IG.Num.DiffLorenzOscillator.GetInitialParameter |
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inlinevirtual |
override double IG.Num.DiffLorenzOscillator.GetFinalParameter |
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inlinevirtual |
override void IG.Num.DiffLorenzOscillator.SetNextStep |
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double |
parameter, |
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double[] |
functionValues |
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) |
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inlinevirtual |
Sets parameters and function values for the next step.
Additional state variables (e.g. history variables) are updated if applicable.
- Parameters
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parameter | Parameter values in the next step. |
functionValues | Function values in the next step. |
Implements IG.Num.DifferentialFirstOrderSystemBase.
override void IG.Num.DiffLorenzOscillator.SaveState |
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double[] |
state | ) |
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inlinevirtual |
override void IG.Num.DiffLorenzOscillator.RestoreState |
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double[] |
state | ) |
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inlinevirtual |
double IG.Num.DiffLorenzOscillator._sigma = 10 |
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protected |
double IG.Num.DiffLorenzOscillator._ro = 28 |
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protected |
double IG.Num.DiffLorenzOscillator._beta = 8.0/3.0 |
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double IG.Num.DiffLorenzOscillator._initialX = 0 |
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double IG.Num.DiffLorenzOscillator._initialY = 0 |
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double IG.Num.DiffLorenzOscillator._initialZ = 0 |
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double IG.Num.DiffLorenzOscillator._initialTime = 0 |
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double IG.Num.DiffLorenzOscillator._finalTime |
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double IG.Num.DiffLorenzOscillator._time |
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double IG.Num.DiffLorenzOscillator._x |
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double IG.Num.DiffLorenzOscillator._y |
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double IG.Num.DiffLorenzOscillator._z |
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override int IG.Num.DiffLorenzOscillator.NumEquations |
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getprotected set |
Number of first orter differential equations that govern the system.
double IG.Num.DiffLorenzOscillator.Sigma |
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getset |
Parameter σ of Lorenz oscillator, the Prandtl number.
double IG.Num.DiffLorenzOscillator.Ro |
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getprotected set |
Parameter ρ of Lorenz oscillator, the Rayleigh number.
double IG.Num.DiffLorenzOscillator.Beta |
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getset |
Parameter β of Lorenz oscillator.
double IG.Num.DiffLorenzOscillator.InitialX |
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getset |
Initial Y coordinate of the system.
double IG.Num.DiffLorenzOscillator.InitialY |
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getset |
Initial Y coordinate of the system.
double IG.Num.DiffLorenzOscillator.InitialZ |
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getset |
Initial Z coordinate of the system.
double IG.Num.DiffLorenzOscillator.InitialTime |
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getset |
double IG.Num.DiffLorenzOscillator.FinalTime |
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getset |
double IG.Num.DiffLorenzOscillator.Time |
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getset |
double IG.Num.DiffLorenzOscillator.X |
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getset |
X coordinate of the current position.
double IG.Num.DiffLorenzOscillator.Y |
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getset |
Y coordinate of the current position.
double IG.Num.DiffLorenzOscillator.Z |
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getset |
Z coordinate of the current position.
The documentation for this class was generated from the following file: