Modelica.Mechanics.MultiBody.Frames.Internal

Information

Package Content

Name	Description
TransformationMatrix
QuaternionBase
maxWithoutEvent	Maximum of the input arguments, without event and without warning message when differentiating
maxWithoutEvent_d	First derivative of function maxWithoutEvent(..)
maxWithoutEvent_dd	First derivative of function maxWithoutEvent_d(..)
resolve1_der	Derivative of function Frames.resolve1(..)
resolve2_der	Derivative of function Frames.resolve2(..)
resolveRelative_der	Derivative of function Frames.resolveRelative(..)

Types and constants

  type TransformationMatrix = Real[3, 3];

  type QuaternionBase = Real[4];

Modelica.Mechanics.MultiBody.Frames.Internal.maxWithoutEvent

Information

Function maxWithoutEvent returns the maximum of its two input arguments. This functions is used instead of the Modelica built-in function "max" or an if-statement with "noEvent(..)", because Dymola prints a warning message when differentiating in these cases. For the special cases as used in the MultiBody library, these warning messages are irrelevant but will potentially irritate the user. The C-function "maxWithoutEvent" and its derivatives provided as additional functions "maxWithoutEvent_d" and "maxWithoutEvent_dd" will not lead to such warning messages.

Inputs

Type	Name	Default	Description
Real	u1
Real	u2

Outputs

Type	Name	Description
Real	y

Modelica definition

function maxWithoutEvent 
  "Maximum of the input arguments, without event and without warning message when differentiating"
  annotation(derivative=maxWithoutEvent_d);

  input Real u1;
  input Real u2;
  output Real y;
  //  annotation (Header="#include \"MultiBody.h\"");
protected 
  Integer dummy;
algorithm 
  y := if u1 > u2 then u1 else u2;
  dummy := 0;
end maxWithoutEvent;

Modelica.Mechanics.MultiBody.Frames.Internal.maxWithoutEvent_d

Inputs

Type	Name	Default	Description
Real	u1
Real	u2
Real	u1_d
Real	u2_d

Outputs

Type	Name	Description
Real	y_d

Modelica definition

function maxWithoutEvent_d 
  "First derivative of function maxWithoutEvent(..)"
  annotation(derivative=maxWithoutEvent_dd);
  input Real u1;
  input Real u2;
  input Real u1_d;
  input Real u2_d;
  output Real y_d;
  //annotation (Header="#include \"MultiBody.h\"");
protected 
  Integer dummy;
algorithm 
  y_d := if u1 > u2 then u1_d else u2_d;
  dummy := 0;
end maxWithoutEvent_d;

Modelica.Mechanics.MultiBody.Frames.Internal.maxWithoutEvent_dd

Inputs

Type	Name	Default	Description
Real	u1
Real	u2
Real	u1_d
Real	u2_d
Real	u1_dd
Real	u2_dd

Outputs

Type	Name	Description
Real	y_dd

Modelica definition

function maxWithoutEvent_dd 
  "First derivative of function maxWithoutEvent_d(..)"
  input Real u1;
  input Real u2;
  input Real u1_d;
  input Real u2_d;
  input Real u1_dd;
  input Real u2_dd;
  output Real y_dd;
algorithm 
  y_dd := if u1 > u2 then u1_dd else u2_dd;
end maxWithoutEvent_dd;

Modelica.Mechanics.MultiBody.Frames.Internal.resolve1_der

Information

Inputs

Type	Name	Default	Description
Orientation	R		Orientation object to rotate frame 1 into frame 2
Real	v2[3]		Vector resolved in frame 2
Real	v2_der[3]		= der(v2)

Outputs

Type	Name	Description
Real	v1_der[3]	Derivative of vector v resolved in frame 1

Modelica definition

function resolve1_der "Derivative of function Frames.resolve1(..)"
  import Modelica.Mechanics.MultiBody.Frames;
  extends Modelica.Icons.Function;
  input Orientation R "Orientation object to rotate frame 1 into frame 2";
  input Real v2[3] "Vector resolved in frame 2";
  input Real v2_der[3] "= der(v2)";
  output Real v1_der[3] "Derivative of vector v resolved in frame 1";
algorithm 
  v1_der := Frames.resolve1(R, v2_der + cross(R.w, v2));
end resolve1_der;

Modelica.Mechanics.MultiBody.Frames.Internal.resolve2_der

Information

Inputs

Type	Name	Default	Description
Orientation	R		Orientation object to rotate frame 1 into frame 2
Real	v1[3]		Vector resolved in frame 1
Real	v1_der[3]		= der(v1)

Outputs

Type	Name	Description
Real	v2_der[3]	Derivative of vector v resolved in frame 2

Modelica definition

function resolve2_der "Derivative of function Frames.resolve2(..)"
  import Modelica.Mechanics.MultiBody.Frames;
  extends Modelica.Icons.Function;
  input Orientation R "Orientation object to rotate frame 1 into frame 2";
  input Real v1[3] "Vector resolved in frame 1";
  input Real v1_der[3] "= der(v1)";
  output Real v2_der[3] "Derivative of vector v resolved in frame 2";
algorithm 
  v2_der := Frames.resolve2(R, v1_der) - cross(R.w, Frames.resolve2(R, v1));
end resolve2_der;

Modelica.Mechanics.MultiBody.Frames.Internal.resolveRelative_der

Information

Inputs

Type	Name	Default	Description
Real	v1[3]		Vector in frame 1
Orientation	R1		Orientation object to rotate frame 0 into frame 1
Orientation	R2		Orientation object to rotate frame 0 into frame 2
Real	v1_der[3]		= der(v1)

Outputs

Type	Name	Description
Real	v2_der[3]	Derivative of vector v resolved in frame 2

Modelica definition

function resolveRelative_der 
  "Derivative of function Frames.resolveRelative(..)"
  import Modelica.Mechanics.MultiBody.Frames;
  extends Modelica.Icons.Function;
  input Real v1[3] "Vector in frame 1";
  input Orientation R1 "Orientation object to rotate frame 0 into frame 1";
  input Orientation R2 "Orientation object to rotate frame 0 into frame 2";
  input Real v1_der[3] "= der(v1)";
  output Real v2_der[3] "Derivative of vector v resolved in frame 2";
algorithm 
  v2_der := Frames.resolveRelative(v1_der+cross(R1.w,v1), R1, R2)
            - cross(R2.w, Frames.resolveRelative(v1, R1, R2));

  /* skew(w) = T*der(T'), -skew(w) = der(T)*T'

     v2 = T2*(T1'*v1)
     der(v2) = der(T2)*T1'*v1 + T2*der(T1')*v1 + T2*T1'*der(v1)
             = der(T2)*T2'*T2*T1'*v1 + T2*T1'*T1*der(T1')*v1 + T2*T1'*der(v1)
             = -w2 x (T2*T1'*v1) + T2*T1'*(w1 x v1) + T2*T1'*der(v1)
             = T2*T1'*(der(v1) + w1 x v1) - w2 x (T2*T1'*v1)
  */
end resolveRelative_der;