Differences

This shows you the differences between two versions of the page.

--- visual3d:documentation:pipeline:model_based_data_commands:angular_momentum_pt [2024/07/16 19:30] – created sgranger
+++ visual3d:documentation:pipeline:model_based_data_commands:angular_momentum_pt [2026/06/02 14:14] (current) – ↷ Links adapted because of a move operation 172.204.27.30
@@ Line 1: / Line 1: @@
-====== ANGULAR_MOMENTUM_PT ======
+====== Angular Momentum about a Point ======
-\\
+This example demonstrates how to calculate the angular momentum of a [[visual3d:documentation:modeling:segments:segment_overview|segment]] about an arbitrary point.
+**Note**: It is very important to note that the total body angular momentum is not calculated by summing the [[visual3d:documentation:visual3d_signal_types:link_model_based_data_type:angular_momentum|ANGULAR_MOMENTUM]] for each segment because this model-based item represents the angular momentum of each segment about its [[visual3d:documentation:modeling:segments:segment_properties#inertial_properties|own centre of mass]]. To calculate the total body angular momentum you must calculate the angular momentum for each segment about the same axis, such as the total body center of mass. The equations in the [[#Angular_Momentum:_About_Total_Body_Center_of_Mass|About Total Body Center of Mass]] section describe how to do this.
-===== Angular Momentum =====
+===== Calculating Angular Momentum =====
-It is important to note that the total body angular momentum is not calculated by summing the [[Visual3D:Documentation:Pipeline:Model_Based_Data_Commands:ANGULAR_MOMENTUM|ANGULAR_MOMENTUM]] for each calculated by the Compute Model Based command. The [[Visual3D:Documentation:Pipeline:Model_Based_Data_Commands:ANGULAR_MOMENTUM|ANGULAR_MOMENTUM]] command calculates the angular momentum about each segment's center of mass, to calculate the total body angular momentum you must calculate the angular momentum for each segment about the same axis, such as the total body center of mass. The equations in the [[#Angular_Momentum:_About_Total_Body_Center_of_Mass|About Total Body Center of Mass]] section describe how to do this.
+Visual3D's built in [[visual3d:documentation:visual3d_signal_types:link_model_based_data_type:angular_momentum|ANGULAR_MOMENTUM]] command calculates the angular momentum of a segment about the segment's center of mass, but angular momentum can also be calculated about a different point in space.
-==== Angular Momentum: About Segment Center of Mass ====
+==== About a Segment's Centre of Mass ====
-Visual3D's built in [[Visual3D:Documentation:Pipeline:Model_Based_Data_Commands:ANGULAR_MOMENTUM|ANGULAR_MOMENTUM]] command calculates the angular momentum of a segment about the segment's center of mass, but angular momentum can also be calculated about a different point in space.
+A segment's angular momentum about its own centre of mass is calculated as:
-**Angular momentum about a segment's center of mass is:**\\
+{{:SegmentAngularMomentumExpression.jpg}}
+where
-|  {{SegmentAngularMomentumExpression.jpg}}  |
+<code>
+I = Moment of Inertia
+w = Angular velocity
+</code>
-==== Angular Momentum: About Total Body Center of Mass ====
+==== About Total Body Center of Mass ====
-**Angular momentum about the total body center of mass is:**\\
+A segment's angular momentum about the total body's centre of mass is calculated as:
+|{{:SegmentAngularMomentum_AboutaPoint_Eq.png}} |{{:SegmentAngularMomentum_AboutaPoint.png}}  |
-**NOTE:** Angular momentum for the whole body about the total body center of mass is just the summation of the angular momentum of **each** segment about the total body center of mass.
+where
-|{{SegmentAngularMomentum_AboutaPoint_Eq.png}}\\ \\ //Iw// = angular momentum of the segment\\ \\ \\ //I// = Moment of Inertia\\ \\ //w// = Angular velocity\\ \\ //r// = distance from the total body center of mass to the segment's center of mass\\ //m// = mass of the segment\\ //v// = translational velocity\\   |{{SegmentAngularMomentum_AboutaPoint.png}}  |
+<code>
+Iw = angular momentum of the segment
+r = distance from the segment's centre of mass to the total body centre of mass
+m = mass of the segment
+v = translational velocity
+</code>
-===== Example Script =====
+**NOTE:** In this case angular momentum for the whole body about the total body center of mass is simply the summation of the angular momentum of **each** segment about the total body center of mass.
-==== Inroduction ====
+===== Example =====
-**To calculate the angular momentum about a point (such as the model center of mass):**
+This example script demonstrates how to calculate a segment's angular momentum about a point, such as the [[visual3d:documentation:visual3d_signal_types:link_model_based_data_type:model_cog|model centre of mass]], by the following steps:
+  - Compute //r//
+  - Compute //mv//
+  - Compute //r// x //mv//
+  - Compute the angular momentum of the segment using the [[visual3d:documentation:visual3d_signal_types:link_model_based_data_type:angular_momentum|Angular Momentum]] command
+  - Compute //Iw// x (//r// x //mv//)
-  - Compute r
+==== Files ====
-  - Compute mv
-  - Compute r x mv
-  - Compute the angular momentum of the segment using the [[Visual3D:Documentation:Pipeline:Model_Based_Data_Commands:ANGULAR_MOMENTUM|Angular Momentum]] command
-  - Compute Iw * (r x mv)
-==== Script ====
 This script and sample CMO files can be downloaded [[https://www.has-motion.com/download/examples/AngularMomentum/AngularMomentum_AboutAPoint.zip|here]]. The download also contains a PDF file with the Angular Momentum equations.
-The following script computes the angular momentum about the total body center of mass, if the user would like to calculate angular momentum about a different point, specify the desired signal in place of "KINETIC_KINEMATIC::MODEL::CenterOfMass".
+==== Script ====
-This script calculates the angular momentum **for each of the listed segments** (RFT+RSK+RTH+LFT+LSK+LTH+RPV).\\
-\\
-If the user would like to calculate the **total body angular momentum about the model center of mass**, the resulting signals from the last Evaluate Expression command for all segments should be summed together. If you would like to calculate the total body angular momentum, you can use the [[Visual3D:Documentation:Pipeline:Signal_Commands:Add_Signals|Add_Signals]] command after the End_For_Each.
 <code>
@@ Line 58: / Line 64: @@
 /RESULT_SUFFIX=_VEL
 ;
-</code>
-<code>
+! Nested Loops
+! Outer Loop gets an active segment
 For_Each
 /ITERATION_PARAMETER_NAME=SEG_NAME
@@ Line 66: / Line 72: @@
 ;
-! compute the R for (r x mv)
+! compute the r for (r x mv)
 Evaluate_Expression
-/EXPRESSION=vector((Kinetic_Kinematic::&::SEG_NAME& ::CGPos::X - KINETIC_KINEMATIC::MODEL::CenterOfMass::X ),
+/EXPRESSION=vector((Kinetic_Kinematic::&::SEG_NAME&:&:CGPos::X - KINETIC_KINEMATIC::MODEL::CenterOfMass::X ), (Kinetic_Kinematic::&::SEG_NAME&:&:CGPos::Y - KINETIC_KINEMATIC::MODEL::CenterOfMass::Y), (Kinetic_Kinematic::&::SEG_NAME&:&:CGPos::Z - KINETIC_KINEMATIC::MODEL::CenterOfMass::Z))
- (Kinetic_Kinematic::&::SEG_NAME& ::CGPos::Y - KINETIC_KINEMATIC::MODEL::CenterOfMass::Y),
- (Kinetic_Kinematic::&::SEG_NAME& ::CGPos::Z - KINETIC_KINEMATIC::MODEL::CenterOfMass::Z))
 /RESULT_NAME=::SEG_NAME&_R
 ! /RESULT_TYPE=DERIVED
@@ Line 78: / Line 82: @@
 ! compute mv
 Evaluate_Expression
-/EXPRESSION=(MODEL::SEGMENT::&::SEG_NAME&:&:MASS)*(Kinetic_Kinematic::&::SEG_NAME& ::CGVel - DERIVED::COM::CENTEROFMASS_VEL )
+/EXPRESSION=(MODEL::SEGMENT::&::SEG_NAME&:&:MASS)*(Kinetic_Kinematic::&::SEG_NAME&:&:CGVel - DERIVED::COM::CENTEROFMASS_VEL)
 /RESULT_NAME=::SEG_NAME&_mv
 ! /RESULT_TYPE=DERIVED
@@ Line 84: / Line 88: @@
 ;
-! compute rxmv
+! compute r x mv
 Evaluate_Expression
 /EXPRESSION=cross(DERIVED::PROCESSED::&::SEG_NAME&_R, DERIVED::PROCESSED::&::SEG_NAME&_mv)
@@ Line 92: / Line 96: @@
 ;
+! compute Iw
 Compute_Model_Based_Data
 /RESULT_NAME=::SEG_NAME&_IW
@@ Line 110: / Line 115: @@
 ;
-! compute rxmv
+! compute Iw x (r x mv)
 Evaluate_Expression
 /EXPRESSION=LINK_MODEL_BASED::ORIGINAL::&::SEG_NAME&_IW + DERIVED::PROCESSED::&::SEG_NAME&_rxmv
@@ Line 117: / Line 122: @@
 /RESULT_FOLDER=Momentum_Contribution
 ;
 End_For_Each
 /ITERATION_PARAMETER_NAME=SEG_NAME
@@ Line 123: / Line 127: @@
 </code>
+The script:
+  - calculates the angular momentum **for each of the listed segments** (RFT+RSK+RTH+LFT+LSK+LTH+RPV). If the user would like to calculate the **total body angular momentum about the model center of mass**, the resulting signals from the last Evaluate Expression command for all segments should be summed together. If you would like to calculate the total body angular momentum, you can use the [[Visual3D:Documentation:Pipeline:Signal_Commands:Add_Signals|Add_Signals]] command after the End_For_Each.
+  - computes the angular momentum about the total body centre of mass, if the user would like to calculate angular momentum about a different point then they simply need to specify the desired signal in place of "KINETIC_KINEMATIC::MODEL::CenterOfMass".