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--- visual3d:documentation:modeling:segments:transforming_segment_moment_of_inertia [2024/06/19 12:49] – sgranger
+++ visual3d:documentation:modeling:segments:transforming_segment_moment_of_inertia [2024/07/17 15:45] (current) – created sgranger
@@ Line 1: / Line 1: @@
-{{{{{{{{{{{{{{{{{{||
+====== Transforming Segment Moment of Inertia ======
-transforming moment of inertia from one coordinate system into another coordinate system
+||
+Transforming moment of inertia from one Coordinate System into Another Coordinate System
 \\
-let the inertia tensor of segment (foot or shank) in it’s own local coordinate system (f) be given:
+Let the Inertia Tensor of Segment (foot or shank) in it’s own local coordinate system (f) be given:
-segmentinertia_1.gif\\
+{{:SegmentInertia_1.gif}}\\
-**note:** these are the values stored in visual3d and viewable in the segment properties.
+**Note:** These are the values stored in Visual3D and viewable in the segment properties.
-find the value of this inertia tensor in any other reference frame (for example, ground) using the following equation:
+Find the value of this inertia tensor in any other reference frame (for example, ground) using the following equation:
-segmentinertia_2.gif\\
+{{:SegmentInertia_2.gif}}\\
-where segmentinertia_3.gif is the rotation matrix that transforms a vector from it's own coordinate system (lcs) to the ground coordinate system
+Where {{:SegmentInertia_3.gif}} is the rotation matrix that transforms a vector from it's own coordinate system (lcs) to the ground coordinate system
-and segmentinertia_4.gif is its transpose.
+and {{:SegmentInertia_4.gif}} is its transpose.
-the above expression does not include the terms due to the parallel axis theorem (segmentinertia_5.gif) which are:
+The above expression does not include the terms due to the parallel axis theorem ({{:SegmentInertia_5.gif}}) which are:
-segmentinertia_6.gif\\
+{{:SegmentInertia_6.gif}}\\
 where the vector s defines the location of hte segment's center of mass relative to ground.
-the total inerties segmentinertia_7.gif for the segment is:
+The total Inerties {{:SegmentInertia_7.gif}} for the segment is:
+{{:SegmentInertia_8.gif}}\\
-segmentinertia_8.gif\\
+To find the total moment of inertia of all segments relative to ground you add the individual segment inertias:
-to find the total moment of inertia of all segments relative to ground you add the individual segment inertias:
+{{:SegmentInertia_9.gif}}\\
-segmentinertia_9.gif\\
+This entire procedure is outlined nicely by Fred Yeadon in the following series of articles.
-this entire procedure is outlined nicely by fred yeadon in the following series of articles.
+**Yeadon, M.R.** (1993). The biomechanics of twisting somersaults. Part I: Rigid body motions. Journal of Sports Sciences 11, 187-198.
-**yeadon, m.r.** (1993). the biomechanics of twisting somersaults. part i: rigid body motions. journal of sports sciences 11, 187-198.
+**Yeadon, M.R.** (1993). The biomechanics of twisting somersaults. Part II: Contact twist. Journal of Sports Sciences 11, 199-208.
-**yeadon, m.r.** (1993). the biomechanics of twisting somersaults. part ii: contact twist. journal of sports sciences 11, 199-208.
+**Yeadon, M.R.** (1993). The biomechanics of twisting somersaults. Part III: Aerial twist. Journal of Sports Sciences 11, 209-218.
-**yeadon, m.r.** (1993). the biomechanics of twisting somersaults. part iii: aerial twist. journal of sports sciences 11, 209-218.
+**Yeadon, M.R.** (1993). The biomechanics of twisting somersaults. Part IV: Partitioning performance using the tilt angle. Journal of Sports Sciences 11, 219-225.
-**yeadon, m.r.** (1993). the biomechanics of twisting somersaults. part iv: partitioning performance using the tilt angle. journal of sports sciences 11, 219-225.
-}}}}}}}}}}}}}}}}}}