QCalc.Math

Library of mathematical functions (e.g., sin, cos), where angle is a quantity

Information

This package contains trigonometric functions that have been copied and modified from Modelica.Math to accept or return angle as a quantity.

Extends from Icons.Package (Icon for standard packages (from MSL 3.2.1)).

Package Contents

Name	Description
$QCalc.Math.acos$ acos	Inverse cosine (-1 ≤ u ≤ 1)
$QCalc.Math.asin$ asin	Inverse sine (-1 ≤ u ≤ 1)
$QCalc.Math.atan$ atan	Inverse tangent
$QCalc.Math.atan2$ atan2	Four quadrant inverse tangent
$QCalc.Math.atan3$ atan3	Four quadrant inverse tangent (with solution closest to given angle y₀)
$QCalc.Math.cos$ cos	Cosine
$QCalc.Math.sin$ sin	Sine
$QCalc.Math.tan$ tan	Tangent (u shall not be -π/2 rad, π/2 rad, 3π/2 rad, …)

$QCalc.Math.acos$ QCalc.Math.acos

Inverse cosine (-1 ≤ u ≤ 1)

$QCalc.Math.acos$

Information

This function returns y = acos(u), with -1 ≤ u ≤ +1, where y is an angle.

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Real	u

Outputs

Type	Name	Description
Angle	y	[ A]

Modelica definition

function acos "Inverse cosine (-1 ≤ u ≤ 1)" extends Modelica.Math.Icons.AxisCenter; input Real u; output Q.Angle y; algorithm y := Modelica.Math.acos(u)*U.rad; end acos;

$QCalc.Math.asin$ QCalc.Math.asin

Inverse sine (-1 ≤ u ≤ 1)

$QCalc.Math.asin$

Information

This function returns y = asin(u), with -1 ≤ u ≤ +1, where y is an angle.

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Real	u

Outputs

Type	Name	Description
Angle	y	[ A]

Modelica definition

function asin "Inverse sine (-1 ≤ u ≤ 1)" extends Modelica.Math.Icons.AxisCenter; input Real u; output Q.Angle y; algorithm y := Modelica.Math.asin(u)*U.rad; end asin;

$QCalc.Math.atan$ QCalc.Math.atan

Inverse tangent

$QCalc.Math.atan$

Information

This function returns y = atan(u), with -∞ < u < ∞, where y is an angle.

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Real	u

Outputs

Type	Name	Description
Angle	y	[ A]

Modelica definition

function atan "Inverse tangent" extends Modelica.Math.Icons.AxisCenter; input Real u; output Q.Angle y; algorithm y := Modelica.Math.atan(u)*U.rad; end atan;

$QCalc.Math.atan2$ QCalc.Math.atan2

Four quadrant inverse tangent

$QCalc.Math.atan2$

Information

This function returns y = atan2(u₁, u₂), where y is an angle, such that tan(y) = u₁/u₂ and y is in the range -π rad < y ≤ π rad. u₂ may be zero, provided u₁ is not zero. Usually u₁, u₂ is provided in such a form that u₁ = sin(y) and u₂ = cos(y).

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Real	u1
Real	u2

Outputs

Type	Name	Description
Angle	y	[ A]

Modelica definition

function atan2 "Four quadrant inverse tangent" extends Modelica.Math.Icons.AxisCenter; input Real u1; input Real u2; output Q.Angle y; algorithm y := Modelica.Math.atan2(u1, u2)*U.rad; end atan2;

$QCalc.Math.atan3$ QCalc.Math.atan3

Four quadrant inverse tangent (with solution closest to given angle y₀)

$QCalc.Math.atan3$

Information

This function returns y = atan2(u₁, u₂, y₀), where y is an angle, such that tan(y) = u₁/u₂ and y is in the range -π rad < y - y₀ ≤ π rad. u₂ may be zero, provided u₁ is not zero.

The difference from atan2() is the optional third argument y₀ that specifies which of the infinite many solutions is returned. Note that for the default case (y₀ = 0), the result is the same as from atan2().

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Real	u1
Real	u2
Angle	y0	0	y shall be in the range: -π < y - y₀ ≤ π [ A]

Outputs

Type	Name	Description
Angle	y	[ A]

Modelica definition

function atan3 "Four quadrant inverse tangent (with solution closest to given angle y₀)" extends Modelica.Math.Icons.AxisCenter; input Real u1; input Real u2; input Q.Angle y0=0 "y shall be in the range: -π < y - y₀ ≤ π"; output Q.Angle y; algorithm y := atan2(u1, u2); if y0 <> 0 then y := y + integer((y0 - y)/U.cyc + 0.5)*U.cyc; end if; // For the default (y0 = 0), return the same result as atan2(). end atan3;

$QCalc.Math.cos$ QCalc.Math.cos

Cosine

$QCalc.Math.cos$

Information

This function returns y = cos(u), where u is an angle.

Extends from Modelica.Math.Icons.AxisLeft (Basic icon for mathematical function with y-axis on left side).

Inputs

Type	Name	Default	Description
Angle	u		[ A]

Outputs

Type	Name	Description
Real	y

Modelica definition

function cos "Cosine" extends Modelica.Math.Icons.AxisLeft; input Q.Angle u; output Real y; algorithm y := Modelica.Math.cos(u/U.rad); end cos;

$QCalc.Math.sin$ QCalc.Math.sin

Sine

$QCalc.Math.sin$

Information

This function returns y = sin(u), where u is an angle.

Extends from Modelica.Math.Icons.AxisLeft (Basic icon for mathematical function with y-axis on left side).

Inputs

Type	Name	Default	Description
Angle	u		[ A]

Outputs

Type	Name	Description
Real	y

Modelica definition

function sin "Sine" extends Modelica.Math.Icons.AxisLeft; input Q.Angle u; output Real y; algorithm y := Modelica.Math.sin(u/U.rad); end sin;

$QCalc.Math.tan$ QCalc.Math.tan

Tangent (u shall not be -π/2 rad, π/2 rad, 3π/2 rad, …)

$QCalc.Math.tan$

Information

This function returns y = tan(u), where u is an angle (if u is a multiple of (n - 1/2) π rad, then y = tan(u) is ±∞).

Extends from Modelica.Math.Icons.AxisCenter (Basic icon for mathematical function with y-axis in the center).

Inputs

Type	Name	Default	Description
Angle	u		[ A]

Outputs

Type	Name	Description
Real	y

Modelica definition

function tan "Tangent (u shall not be -π/2 rad, π/2 rad, 3π/2 rad, …)" extends Modelica.Math.Icons.AxisCenter; input Q.Angle u; output Real y; algorithm y := Modelica.Math.tan(u/U.rad); end tan;

Library Contents

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QCalc.Math

Information

Package Contents

QCalc.Math.acos

Information

Inputs

Outputs

Modelica definition

QCalc.Math.asin

Information

Inputs

Outputs

Modelica definition

QCalc.Math.atan

Information

Inputs

Outputs

Modelica definition

QCalc.Math.atan2

Information

Inputs

Outputs

Modelica definition

QCalc.Math.atan3

Information

Inputs

Outputs

Modelica definition

QCalc.Math.cos

Information

Inputs

Outputs

Modelica definition

QCalc.Math.sin

Information

Inputs

Outputs

Modelica definition

QCalc.Math.tan

Information

Inputs

Outputs

Modelica definition

$QCalc.Math.acos$ QCalc.Math.acos

$QCalc.Math.asin$ QCalc.Math.asin

$QCalc.Math.atan$ QCalc.Math.atan

$QCalc.Math.atan2$ QCalc.Math.atan2

$QCalc.Math.atan3$ QCalc.Math.atan3

$QCalc.Math.cos$ QCalc.Math.cos

$QCalc.Math.sin$ QCalc.Math.sin

$QCalc.Math.tan$ QCalc.Math.tan