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# Polyhedron Inertial Properties 1.0

Date Added: August 28, 2013  |  Visits: 276
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Dynamical analyses in engineering often require inertial properties of complex shapes such as polyhedra. The volume, the first moment of volume and the second moment of volume of a general solid can be computed by V = Integral( dVol ), VR = Integral( R*dVol ), VRR = Integral( R*Rd-deOao*dVol ). Also of interest are the centroidal radius RC = VR/V and the inertia tensor I = eye(3,3)*trace( VRR )-VRR. The Gauss divergence theorem for a tensor function F states that Integral( div(F)*dVol ) = SurfIntegral( Dot(N,F)*dSurf ) where R = [x; y; z] is the cartesian radius vector and N is the outward directed unit surface normal. This leads to [V, VR, VRR] = SurfIntegral( [ 1/3, R/4, R*Rd-deOao/5 ]*Dot(N,R)*dSurf ). The surface parts of a polyhedron have constant surface normals and the integrals over planar parts can be converted to line integrals and evaluated exactly. A concise algorithm for the inertial properties of arbitrary polyhedra results. General shapes can be approximated using polyhedral models. However, obtaining several digit accuracy for curved surfaces such as a sphere or a torus may require a large number of elements. Examples in the program show exact results for several polyhedra and approximate results for curved surfaces. Among the utility functions provided are POLHEDRN to compute polyhedron properties using corner coordinates of the faces, SRFVN employing x,y,z arrays similar to function surf, and POLYXY which obtains inertial properties of arbitrary polygons. More detail on the methods used appear in 'Advanced Mathematics and Mechanics Applications Using MATLAB', 3rd Ed.,2003, CRC Press, by H. Wilson, L. Turcotte, and D. Halpern. RUNPOLYHEDRON is the main driver function showing demo examples

 Requirements: No special requirements Platforms: Matlab Keyword: 13 R4,  3rd Ed2003,  Accuracy,  Advanced Mathematics,  Algorithm,  Also Of,  Among The,  Analyses,  Approximate Results,  Approximated,  Arbitrary Polygons,  Arbitrary Polyhedra,  Are The,  Eye Trace,  Integral,  Obtains Inertial,  Surfintegral,  Vrv,  Xyz Arrays Similar Users rating: 0/10

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