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--- visual3d:documentation:modeling:segments:transforming_segment_moment_of_inertia [2024/07/17 15:42] – removed sgranger
+++ visual3d:documentation:modeling:segments:transforming_segment_moment_of_inertia [2024/07/17 15:45] (current) – created sgranger
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+====== Transforming Segment Moment of Inertia ======
+||
+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:
+{{:SegmentInertia_1.gif}}\\
+**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:
+{{: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
+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:
+{{: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:
+{{: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}}\\
+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 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 IV: Partitioning performance using the tilt angle. Journal of Sports Sciences 11, 219-225.