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--- visual3d:documentation:modeling:segments:transforming_segment_moment_of_inertia [2024/06/17 18:17] – created 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 ======
 ||
@@ Line 10: / Line 10: @@
 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}}\\
@@ Line 17: / Line 17: @@
 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:
-[[SegmentInertia_9.gif]]\\
+{{:SegmentInertia_9.gif}}\\
@@ Line 50: / Line 50: @@
 **Yeadon, M.R.** (1993). The biomechanics of twisting somersaults. Part IV: Partitioning performance using the tilt angle. Journal of Sports Sciences 11, 219-225.