Changeset 1073 for trunk

Timestamp:

02/26/08 09:21:13 (6 months ago)

Author:

dietmarw

Message:

* special symbols where encoded in UTF-8 by mistake during the last commit
* also corrected some Umlauts to HTML entities when present in the HTML environment

Location:

trunk/Modelica

Files:

• Blocks/package.mo (modified) (29 diffs)
• Electrical/Digital.mo (modified) (1 diff)
• Mechanics/MultiBody/package.mo (modified) (43 diffs)
• Media/package.mo (modified) (1 diff)
• SIunits.mo (modified) (10 diffs)
• Thermal/FluidHeatFlow.mo (modified) (1 diff)
• Thermal/HeatTransfer.mo (modified) (44 diffs)
• package.mo (modified) (1 diff)

trunk/Modelica/Blocks/package.mo

@@ -8 +8 @@
 
 annotation (
-  Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}), 
+  Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,100}}),
       graphics={
       Rectangle(extent={{-32,-6},{16,-35}}, lineColor={0,0,0}),
@@ -44 +44 @@
 <i>This Modelica package is <b>free</b> software; it can be redistributed and/or modified
 under the terms of the <b>Modelica license</b>, see the license conditions
-and the accompanying <b>disclaimer</b> 
+and the accompanying <b>disclaimer</b>
 <a href=\"Modelica://Modelica.UsersGuide.ModelicaLicense\">here</a>.</i>
 </p>
@@ -108 +108 @@
       initType=Modelica.Blocks.Types.Init.SteadyState,
       limitsAtInit=false,
-      controllerType=Modelica.Blocks.Types.SimpleController.PI) 
+      controllerType=Modelica.Blocks.Types.SimpleController.PI)
       annotation (Placement(transformation(extent={{-56,-20},{-36,0}}, rotation=
              0)));
@@ -158 +158 @@
 
 <li> The output of the controller is a torque that drives a motor inertia
-     \"inertia1\". Via a complï¿œiant spring/damper component, the load
+     \"inertia1\". Via a compliant spring/damper component, the load
      inertia \"inertia2\" is attached. A constant external torque of 10 Nm
      is acting on the load inertia.</li>
@@ -166 +166 @@
 The PI controller settings included \"limitAtInit=false\", in order that
 the controller output limits of 12 Nm are removed from the initialization
-problem. 
+problem.
 </p>
 
@@ -204 +204 @@
 </html>"));
 
-    Modelica.Mechanics.Rotational.Sources.Torque torque 
+    Modelica.Mechanics.Rotational.Sources.Torque torque
       annotation (Placement(transformation(extent={{-25,-20},{-5,0}}, rotation=
               0)));
@@ -210 +210 @@
                                                       c=1e4, d=100,
       stateSelect=StateSelect.prefer,
-      w_rel(fixed=true)) 
+      w_rel(fixed=true))
       annotation (Placement(transformation(extent={{32,-20},{52,0}}, rotation=0)));
     Modelica.Mechanics.Rotational.Components.Inertia inertia2(
-                                                   J=2) 
+                                                   J=2)
       annotation (Placement(transformation(extent={{60,-20},{80,0}}, rotation=0)));
     Modelica.Blocks.Sources.KinematicPTP kinematicPTP(startTime=0.5, deltaq={
@@ -223 +223 @@
           Types.Init.InitialState) annotation (Placement(transformation(extent=
               {{-63,20},{-43,40}}, rotation=0)));
-    Modelica.Mechanics.Rotational.Sensors.SpeedSensor speedSensor 
+    Modelica.Mechanics.Rotational.Sensors.SpeedSensor speedSensor
       annotation (Placement(transformation(extent={{22,-50},{2,-30}}, rotation=
               0)));
     Modelica.Mechanics.Rotational.Sources.ConstantTorque loadTorque(
                                                             tau_constant=10,
-        useSupport=false) 
+        useSupport=false)
       annotation (Placement(transformation(extent={{98,-15},{88,-5}}, rotation=
               0)));
@@ -234 +234 @@
     der(spring.w_rel) = 0;
   equation
-    connect(spring.flange_b,inertia2. flange_a) 
+    connect(spring.flange_b,inertia2. flange_a)
       annotation (Line(points={{52,-10},{60,-10}}, color={0,0,0}));
-    connect(inertia1.flange_b, spring.flange_a) 
+    connect(inertia1.flange_b, spring.flange_a)
       annotation (Line(points={{22,-10},{32,-10}}, color={0,0,0}));
-    connect(torque.flange, inertia1.flange_a) 
+    connect(torque.flange, inertia1.flange_a)
       annotation (Line(points={{-5,-10},{2,-10}}, color={0,0,0}));
     connect(kinematicPTP.y[1], integrator.u) annotation (Line(points={{-71,30},
             {-65,30}}, color={0,0,127}));
-    connect(speedSensor.flange, inertia1.flange_b) 
+    connect(speedSensor.flange, inertia1.flange_b)
       annotation (Line(points={{22,-40},{22,-10}}, color={0,0,0}));
-    connect(loadTorque.flange, inertia2.flange_b) 
+    connect(loadTorque.flange, inertia2.flange_b)
       annotation (Line(points={{88,-10},{80,-10}}, color={0,0,0}));
     connect(PI.y, torque.tau)  annotation (Line(points={{-35,-10},{-27,-10}},
@@ -271 +271 @@
 <p>
 This example demonstrates how to construct an inverse model in Modelica
-(for more details see <a href=\"http://www.modelica.org/events/Conference2005/online_proceedings/Session3/Session3c3.pdf\">Looye, Thï¿œmmel, Kurze, Otter, Bals: Nonlinear Inverse Models for Control</a>).
+(for more details see <a href=\"http://www.modelica.org/events/Conference2005/online_proceedings/Session3/Session3c3.pdf\">Looye, Th&uuml;mmel, Kurze, Otter, Bals: Nonlinear Inverse Models for Control</a>).
 </p>
 
@@ -295 +295 @@
 numerator polynomial n(s) (which is usually the case for plant models),
 then the inverse model is no longer proper, i.e., it is not causal.
-To avoid this, an approximate inverse model is constructed by adding 
+To avoid this, an approximate inverse model is constructed by adding
 a sufficient number of poles to the denominator of the inverse model.
 This can be interpreted as filtering the desired output signal y:
@@ -323 +323 @@
 For this, the sine signal \"sin\" is first filtered with a \"CriticalDamping\"
 filter of order 1 and then the output of this filter is connected to the output
-of the \"firstOrder1\" block (via the InverseBlockConstraints block, since 
+of the \"firstOrder1\" block (via the InverseBlockConstraints block, since
 2 outputs cannot be connected directly together in a block diagram).
 </p>
@@ -330 +330 @@
 In order to check the inversion, the computed input of \"firstOrder1\" is used
 as input in an identical block \"firstOrder2\". The output of \"firstOrder2\" should
-be the given \"sine\" function. The difference is constructed with the \"feedback\" 
+be the given \"sine\" function. The difference is constructed with the \"feedback\"
 block. Since the \"sine\" function is filtered, one cannot expect that this difference
-is zero. The higher the cut-off frequency of the filter, the closer is the 
+is zero. The higher the cut-off frequency of the filter, the closer is the
 agreement. A typical simulation result is shown in the next figure:
 </p>
@@ -386 +386 @@
     "Demonstrates the usage of logical sources together with their diagram animation"
        extends Modelica.Icons.Example;
-       Sources.BooleanTable table(table={2,4,6,8}) 
+       Sources.BooleanTable table(table={2,4,6,8})
                                        annotation (Placement(transformation(
             extent={{-60,-100},{-40,-80}}, rotation=0)));
@@ -401 +401 @@
       Documentation(info="<html>
 <p>
-This simple example demonstrates the logical sources in 
+This simple example demonstrates the logical sources in
 <a href=\"Modelica://Modelica.Blocks.Sources\">Modelica.Blocks.Sources</a> and demonstrate
 their diagram animation (see \"small circle\" close to the output connector).
@@ -415 +415 @@
             extent={{-60,-60},{-40,-40}}, rotation=0)));
       Sources.BooleanExpression booleanExpression(
-                                                y=pulse.y and step.y) 
+                                                y=pulse.y and step.y)
       annotation (Placement(transformation(extent={{20,20},{80,40}}, rotation=0)));
      end ShowLogicalSources;
@@ -515 +515 @@
 In <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage_Utilities.Interfaces\">Modelica.Blocks.Examples.BusUsage_Utilities.Interfaces</a>
 the buses for this example are defined. Both the \"ControlBus\" and the \"SubControlBus\" are
-<b>expandable</b> connectors that do not define any variable. For example, 
+<b>expandable</b> connectors that do not define any variable. For example,
 <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage_Utilities.Interfaces.ControlBus#text\">Interfaces.ControlBus</a>
 is defined as:
@@ -521 +521 @@
 <pre>  <b>expandable connector</b> ControlBus
       <b>extends</b> Modelica.Icons.ControlBus;
-      <b>annotation</b> (Icon(Rectangle(extent=[-20, 2; 22, -2], 
+      <b>annotation</b> (Icon(Rectangle(extent=[-20, 2; 22, -2],
                        style(rgbcolor={255,204,51}, thickness=0.5))));
   <b>end</b> ControlBus;
@@ -527 +527 @@
 <p>
 Note, the \"annotation\" in the connector is important since the color
-and thickness of a connector line are taken from the first 
+and thickness of a connector line are taken from the first
 line element in the icon annotation of a connector class. Above, a small rectangle in the
 color of the bus is defined (and therefore this rectangle is not
@@ -547 +547 @@
 
 <p>
-The \"Add variable/New name\" field allows the user to define the name of the signal on 
+The \"Add variable/New name\" field allows the user to define the name of the signal on
 the \"controlBus\". When typing \"realSignal1\" as \"New name\", a connection of the form:
 </p>
@@ -556 +556 @@
 <p>
 is generated and the \"controlBus\" contains the new signal \"realSignal1\". Modelica tools
-may give more support in order to list potential signals for a connection. 
+may give more support in order to list potential signals for a connection.
 For example, in Dymola all variables are listed in the menu that are contained in
 connectors which are derived by inheritance from \"controlBus\". Therefore, in
@@ -564 +564 @@
 </p>
 
-<pre>  <b>expandable connector</b> StandardControlBus 
+<pre>  <b>expandable connector</b> StandardControlBus
     <b>extends</b> BusUsage_Utilities.Interfaces.ControlBus;
-  
+
     <b>import</b> SI = Modelica.SIunits;
     SI.AngularVelocity    realSignal1   \"First Real signal\";
@@ -598 +598 @@
       startTime=0.5)   annotation (Placement(transformation(extent={{-60,-40},{
               -40,-20}}, rotation=0)));
-    Modelica.Blocks.Sources.BooleanStep booleanStep(startTime=0.5) 
+    Modelica.Blocks.Sources.BooleanStep booleanStep(startTime=0.5)
                                                                annotation (Placement(
           transformation(extent={{-58,0},{-38,20}}, rotation=0)));
-    Modelica.Blocks.Sources.Sine sine 
+    Modelica.Blocks.Sources.Sine sine
                                      annotation (Placement(transformation(
             extent={{-60,40},{-40,60}}, rotation=0)));
 
-    Modelica.Blocks.Examples.BusUsage_Utilities.Part part 
+    Modelica.Blocks.Examples.BusUsage_Utilities.Part part
               annotation (Placement(transformation(extent={{-60,-80},{-40,-60}},
             rotation=0)));
-    Modelica.Blocks.Math.Gain gain 
+    Modelica.Blocks.Math.Gain gain
       annotation (Placement(transformation(extent={{-40,70},{-60,90}}, rotation=
              0)));
   protected
-    BusUsage_Utilities.Interfaces.ControlBus controlBus 
+    BusUsage_Utilities.Interfaces.ControlBus controlBus
       annotation (Placement(transformation(
           origin={30,10},
@@ -670 +670 @@
 <p>
 This connector defines the \"expandable connector\" ControlBus that
-is used as bus in the 
+is used as bus in the
 <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage\">BusUsage</a> example.
 Note, this connector is \"empty\". When using it, the actual content is
@@ -692 +692 @@
 <p>
 This connector defines the \"expandable connector\" SubControlBus that
-is used as sub-bus in the 
+is used as sub-bus in the
 <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage\">BusUsage</a> example.
 Note, this connector is \"empty\". When using it, the actual content is
@@ -724 +724 @@
 <p>
 This connector is used to show default signals that might be added
-to the 
+to the
 <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage_Utilities.Interfaces.ControlBus\">ControlBus</a>.
 </p>
@@ -747 +747 @@
 <p>
 This connector is used to show default signals that might be added
-to the 
+to the
 <a href=\"Modelica://Modelica.Blocks.Examples.BusUsage_Utilities.Interfaces.SubControlBus\">SubControlBus</a>.
 </p>
@@ -758 +758 @@
 The bus definitions in this package are the default definitions shown in the
 bus menu when connecting a signal to an expandable connector (here: ControlBus
-or SubControlBus). Usually, the connectors of this package should not be 
+or SubControlBus). Usually, the connectors of this package should not be
 utilized by a user.
 </p>
@@ -795 +795 @@
 </p>
 </html>"));
-     Interfaces.SubControlBus subControlBus 
+     Interfaces.SubControlBus subControlBus
        annotation (Placement(transformation(
             origin={100,0},
             extent={{-20,-20},{20,20}},
             rotation=270)));
-     Sources.RealExpression realExpression(y=time) 
+     Sources.RealExpression realExpression(y=time)
        annotation (Placement(transformation(extent={{-6,0},{20,20}}, rotation=0)));
-     Sources.BooleanExpression booleanExpression(y=time > 0.5) 
+     Sources.BooleanExpression booleanExpression(y=time > 0.5)
        annotation (Placement(transformation(extent={{-6,-30},{20,-10}},
               rotation=0)));

trunk/Modelica/Electrical/Digital.mo

@@ -4395 +4395 @@
       parameter Real value_L(start=0) "value for digital L (Weak    0)";
       parameter Real value_H(start=1) "value for digital H (Weak    1)";
-      parameter Real value_m(start=0.5) "value for digital m (Donï¿œt care)";
+      parameter Real value_m(start=0.5) "value for digital m (DonŽt care)";
       annotation (Documentation(info="<HTML>
 <P>

trunk/Modelica/Mechanics/MultiBody/package.mo

@@ -16 +16 @@
 3-dimensional mechanical components to model in a convenient way
 <b>mechanical systems</b>, such as robots, mechanisms, vehicles.
-Typical animations generated with this library are shown 
+Typical animations generated with this library are shown
 in the next figure:
 </p>
@@ -38 +38 @@
 <i>This Modelica package is <b>free</b> software; it can be redistributed and/or modified
 under the terms of the <b>Modelica license</b>, see the license conditions
-and the accompanying <b>disclaimer</b> 
+and the accompanying <b>disclaimer</b>
 <a href=\"Modelica://Modelica.UsersGuide.ModelicaLicense\">here</a>.</i>
 </p><br>
@@ -98 +98 @@
 </li>
 <li>
-<a href=\"Modelica://Modelica.Mechanics.MultiBody.UsersGuide.Tutorial.FirstExample\">A first example</a> 
+<a href=\"Modelica://Modelica.Mechanics.MultiBody.UsersGuide.Tutorial.FirstExample\">A first example</a>
   describes in detail all the steps to build a simple pendulum model.
 </li>
@@ -334 +334 @@
 <p>
 In principal, now special action is needed, if
-loop structures occur (contrary to the ModelicaAdditions.MultiBody library). 
-An example is presented in the figure below. It is available as 
+loop structures occur (contrary to the ModelicaAdditions.MultiBody library).
+An example is presented in the figure below. It is available as
 <a href=\"Modelica://Modelica.Mechanics.MultiBody.Examples.Loops.Fourbar1\">
 MultiBody.Examples.Loops.Fourbar1</a>
@@ -343 +343 @@
 </p>
 <p>
-This mechanism consists of 6 revolute joints, 1 prismatic joint and forms a 
-kinematical loop. 
-It has has one degree of freedom. In the next figure the default animation 
-is shown. Note, that the axes of the revolute joints are represented by the 
-red cylinders and that the axis of the prismatic joint is represented by the 
-red box on the lower right side. 
+This mechanism consists of 6 revolute joints, 1 prismatic joint and forms a
+kinematical loop.
+It has has one degree of freedom. In the next figure the default animation
+is shown. Note, that the axes of the revolute joints are represented by the
+red cylinders and that the axis of the prismatic joint is represented by the
+red box on the lower right side.
 </p>
 <p align=\"center\">
@@ -354 +354 @@
 </p>
 <p>
-Whenever loop structures occur, non-linear algebraic 
-equations are present on \"position level\". It is then usually not possible by 
-structural analysis to select states during translation (which is possible for 
-non-loop structures). In the example above, Dymola detects a non-linear 
-algebraic loop of 57 equations and reduces this to a system of 7 coupled 
-algebraic equations. Note, that this is performed without using any 
-\"cut-joints\" as it is usually done in multi-body programs, but by just 
-appropriate symbolic equation manipulation. Via the dynamic dummy derivative 
-method the generalized coordinates on position and velocity level from one of 
-the 7 joints are dynamically selected as states during simulation. Whenever, 
-these two states are no longer appropriate, states from one of the other 
+Whenever loop structures occur, non-linear algebraic
+equations are present on \"position level\". It is then usually not possible by
+structural analysis to select states during translation (which is possible for
+non-loop structures). In the example above, Dymola detects a non-linear
+algebraic loop of 57 equations and reduces this to a system of 7 coupled
+algebraic equations. Note, that this is performed without using any
+\"cut-joints\" as it is usually done in multi-body programs, but by just
+appropriate symbolic equation manipulation. Via the dynamic dummy derivative
+method the generalized coordinates on position and velocity level from one of
+the 7 joints are dynamically selected as states during simulation. Whenever,
+these two states are no longer appropriate, states from one of the other
 joints are selected during simulation.
 </p>
 <p>
-The efficiency of loop structures can usually be 
-enhanced, if states are statically fixed at translation time. For this 
-mechanism, the generalized coordinates of joint j1 (i.e., the 
-rotation angle of the revolute joint and its derivative) can always be used as 
-states. This can be stated by setting parameter \"enforceStates = <b>true</b>\" 
-in the \"Advanced\" menu of the desired joint. This flag sets the attribute 
-stateSelect of the generalized coordinates of the coresponding joint to 
-\"StateSelect.always\". When setting this flag to <b>true</b> for joint j1 in 
-the four bar mechanism, Dymola detects a non-linear algebraic loop of 40 
-equations and reduces this to a system of 5 coupled non-linear algebraic 
+The efficiency of loop structures can usually be
+enhanced, if states are statically fixed at translation time. For this
+mechanism, the generalized coordinates of joint j1 (i.e., the
+rotation angle of the revolute joint and its derivative) can always be used as
+states. This can be stated by setting parameter \"enforceStates = <b>true</b>\"
+in the \"Advanced\" menu of the desired joint. This flag sets the attribute
+stateSelect of the generalized coordinates of the coresponding joint to
+\"StateSelect.always\". When setting this flag to <b>true</b> for joint j1 in
+the four bar mechanism, Dymola detects a non-linear algebraic loop of 40
+equations and reduces this to a system of 5 coupled non-linear algebraic
 equations.
 </p>
@@ -384 +384 @@
 equations analytically. For a certain class of systems this can
 be performed also with the MultiBody library. This technique
-is described in section 
+is described in section
 \"<a href=\"AnalyticLoopHandling\">Analytic loop handling</a>\".
 </p>
@@ -394 +394 @@
         annotation (Documentation(info="<HTML>
 <p>
-In the figure below, the model of a V6 engine is 
-shown that has a simple combustion model. It is available as 
+In the figure below, the model of a V6 engine is
+shown that has a simple combustion model. It is available as
 <a href=\"Modelica://Modelica.Mechanics.MultiBody.Examples.Loops.EngineV6\">
-MultiBody.Examples.Loops.EngineV6</a>. 
+MultiBody.Examples.Loops.EngineV6</a>.
 </p>
 <p align=\"center\">
@@ -403 +403 @@
 </p>
 <p>
-The Modelica schematic of one cylinder 
-is given in the figure below. Connecting 6 instances of this 
+The Modelica schematic of one cylinder
+is given in the figure below. Connecting 6 instances of this
 cylinder appropriately together results in the engine schematic displayed
 above.
@@ -412 +412 @@
 </p>
 <p>
-In the next figure the animation of the engine is 
-shown. Every cylinder consists essentially of 1 prismatic and 2 revolute 
-joints that form a planar loop, since the axes of the two revolute joints are 
-parallel to each other and the axis of the prismatic joint is orthogonal to 
-the revolute joint axes. All 6 cylinders together form a coupled set of 6 
-loops that have together 1 degree of freedom. 
+In the next figure the animation of the engine is
+shown. Every cylinder consists essentially of 1 prismatic and 2 revolute
+joints that form a planar loop, since the axes of the two revolute joints are
+parallel to each other and the axis of the prismatic joint is orthogonal to
+the revolute joint axes. All 6 cylinders together form a coupled set of 6
+loops that have together 1 degree of freedom.
 </p>
 <p align=\"center\">
@@ -423 +423 @@
 </p>
 <p>
-All planar loops, and especially the engine, result in 
+All planar loops, and especially the engine, result in
 a DAE (= Differential-Algebraic Equation system)
-that does not have a unique solution. The reason is that, e.g., the cut 
-forces in direction of the axes of the revolute joints cannot be uniquely 
-computed. Any value fulfills the DAE equations. This is a structural property 
-that is determined by the symbolic algorithms. Since they detect that the DAE is 
-structurally singular, a further processing is not possible. Without 
-additional information it is also impossible that the symbolic algorithms 
-could be enhanced because if the axes of rotations of the revolute joints are 
-only slightly changed such that they are no longer parallel to each other, the 
-planar loop can no longer move and has 0 degrees of freedom. Algorithms based 
-on pure structural information cannot distinguish these two cases. 
-</p>
-<p>
-The usual remedy is to remove superfluous constraints, 
-e.g., along the axis of rotation of <b>one</b> revolute joint. Since this is 
+that does not have a unique solution. The reason is that, e.g., the cut
+forces in direction of the axes of the revolute joints cannot be uniquely
+computed. Any value fulfills the DAE equations. This is a structural property
+that is determined by the symbolic algorithms. Since they detect that the DAE is
+structurally singular, a further processing is not possible. Without
+additional information it is also impossible that the symbolic algorithms
+could be enhanced because if the axes of rotations of the revolute joints are
+only slightly changed such that they are no longer parallel to each other, the
+planar loop can no longer move and has 0 degrees of freedom. Algorithms based
+on pure structural information cannot distinguish these two cases.
+</p>
+<p>
+The usual remedy is to remove superfluous constraints,
+e.g., along the axis of rotation of <b>one</b> revolute joint. Since this is
 not easy for an inexperienced modeler, the special joint:
 <a href=\"Modelica://Modelica.Mechanics.MultiBody.Joints.RevolutePlanarLoopConstraint\">
-RevolutePlanarLoopConstraint</a> is provided that removes these constraints. 
+RevolutePlanarLoopConstraint</a> is provided that removes these constraints.
 Exactly one revolute joint in a every planar loop must be replaced by this
 joint type. In the engine example, this special joinst is used for
@@ -448 +448 @@
 </p>
 <p>
-If a modeler is not aware of the problems with planar 
+If a modeler is not aware of the problems with planar
 loops and models them without special consideration, a Modelica
-translator, such as Dymola, displays an error 
-message and points out that a planar loop may be the reason and suggests to 
+translator, such as Dymola, displays an error
+message and points out that a planar loop may be the reason and suggests to
 use the RevolutePlanarLoopConstraint joint.
-This error message is due to an annotation in 
+This error message is due to an annotation in
 the Frame connector.
 </p>
@@ -463 +463 @@
 </pre>
 <p>
-If no assignment can be found for some 
-forces in a connector, the \"unassignedMessage\" is displayed. In most cases the 
-reason for this is a planar loop or two joints that constrain the same motion. 
+If no assignment can be found for some
+forces in a connector, the \"unassignedMessage\" is displayed. In most cases the
+reason for this is a planar loop or two joints that constrain the same motion.
 Both cases are discussed in the error message.
 </p>
 <p>
-Note, that the non-linear algebraic equations occurring 
-in planar loops can be solved analytically in most cases and therefore it is 
+Note, that the non-linear algebraic equations occurring
+in planar loops can be solved analytically in most cases and therefore it is
 highly recommended to use the techniques discussed in section
 \"<a href=\"AnalyticLoopHandling\">Analytic loop handling</a>\"
@@ -481 +481 @@
 
         annotation (Documentation(info="<HTML>
-It is well known that the non-linear 
-algebraic equations of most mechanical loops in technical devices can be 
-solved analytically. It is, however, difficult to perform this fully 
-automatically and therefore none of the commercial, general purpose multi-body 
-programs, such as MSC ADAMS, LMS DADS, SIMPACK, have this feature. 
-These programs solve loop structures with pure numerical methods. Multi-body 
-programs that are designed for real-time simulation of the dynamics of 
-specific vehicles, such as ve-DYNA, usually contain manual implementations 
-of a particular multi-body system (the vehicle) where the occurring loops are 
-either analytically solved, if this is possible, or are treated by table 
-look-up where the tables are constructed in a pre-processing phase. Without 
-these features the required real-time capability would be difficult to 
+It is well known that the non-linear
+algebraic equations of most mechanical loops in technical devices can be
+solved analytically. It is, however, difficult to perform this fully
+automatically and therefore none of the commercial, general purpose multi-body
+programs, such as MSC ADAMS, LMS DADS, SIMPACK, have this feature.
+These programs solve loop structures with pure numerical methods. Multi-body
+programs that are designed for real-time simulation of the dynamics of
+specific vehicles, such as ve-DYNA, usually contain manual implementations
+of a particular multi-body system (the vehicle) where the occurring loops are
+either analytically solved, if this is possible, or are treated by table
+look-up where the tables are constructed in a pre-processing phase. Without
+these features the required real-time capability would be difficult to
 achieve.
 </p>
@@ -499 +499 @@
 Prof. Hiller and his group in Duisburg, Germany,
 have developed systematic methods to handle mechanical
-loops analytically. The \"characteristic pair of joints\" method 
-basically cuts a loop at two joints and uses geometric 
-invariants to reduce the number of algebraic 
-equations, often down to one equation that can be solved analytically. Also 
-several multi-body codes have been developed that are based on this method, 
-e.g., MOBILE. Besides the very desired feature to solve non-linear 
-algebraic equations analytically, i.e., effic