Mechanics: Statics Distributed Force 3D Body Centroid of 3D Body by Integration Draft for Information Only
Content
Centroid of 3D Body
Centroid of 3D BodyThe centroid of 3D Body is determined by the first moment of a three dimensional body with the method of the first moment of volume. Centroids of VolumesVolume by IntegrationVolume by Triple IntegrationFor example, the signed volume of the 3D region U is bounded by surfaces in rectangular form , Imply An elemental volume ΔV in rectangular form can be defined as Δx times Δy times Gz. Imply Therefore the volume of the solid cone U in cartesian coordinates xyz is equal to In general, the volume of a region can be determined by multiple integration through sweeping the signed elemental volume starting from along any one of the rectangular coordinate axes. Imply Starting from horizontal sweeping along x axis Considering an elemental volume along x axis. Imply All elemental volumes can be bounded by curves in the plane yz. And the curves is Similarly sweeping the elemental volume ΔVyz along y axis horizontally. Considering an elemental volume ΔVz along y axis. Imply Since the bounding curves are joined at plane zx, The bounds of the bounding curves are Therefore the volume of the solid cone U is The volume of the solid cone U can also be determined starting from other axis. Starting from horizontal sweeping along y axis Considering an elemental volume along y axis. Imply All elemental volumes in z direction can be bounded by curves in the plane zx. And the curves is Similarly sweeping the elemental volume ΔVzx along z axis vertically. Considering an elemental volume ΔVx along z axis. Imply The bounding curves in x direction can also be bounded at plane zx. The bounds of the bounding curves are The volume of the solid cone U can be expressed as Therefore the volume of the solid cone U is
©sideway ID: 120600011 Last Updated: 21/6/2012 Revision: 0 Ref: References
Latest Updated Links

Home_{ 5} Business Management HBR_{ 3} Information Recreation Hobbies_{ 7} Culture Chinese_{ 1097} English_{ 337} Reference_{ 67} Computer Hardware_{ 149} Software Application_{ 187} Digitization_{ 24} Numeric_{ 19} Programming Web_{ 757} CSS_{ 1} ASP.NET_{ 1} Regular Expression_{ 1} HTML Knowledge Base Common Color_{ 1} Html 401 Special_{ 1} OS_{ 389} MS Windows Windows10_{ 1} .NET Framework_{ 1} DeskTop_{ 7} Knowledge Mathematics Formulas_{ 8} Algebra_{ 20} Number Theory_{ 206} Trigonometry_{ 18} Geometry_{ 18} Calculus_{ 67} Complex Analysis_{ 21} Engineering Tables_{ 8} Mechanical Mechanics_{ 1} Rigid Bodies Statics_{ 92} Dynamics_{ 37} Fluid_{ 5} Fluid Kinematics_{ 5} Control Process Control_{ 1} Acoustics_{ 19} FiniteElement_{ 2} Physics Electric_{ 10} Biology_{ 1} Geography_{ 1} 
Copyright © 20002019 Sideway . All rights reserved Disclaimers last modified on 06 September 2019