5
$\begingroup$

With cylinder I have:

 body = Cylinder[{{-l/2, 0, 0}, {l/2, 0, 0}}, r];
 (\[ScriptCapitalI] = \[Rho] MomentOfInertia[body, 
 Assumptions -> l > 0 && w > 0 && h > 0]) // MatrixForm; 
 m Cancel[\[ScriptCapitalI]/(\[Rho] Volume[body])] // MatrixForm(*Code from MMA help*)

 (*{{(m*r^2)/2, 0, 0}, {0, (m*(l^2 + 3*r^2))/12, 0}, {0, 0, (m*(l^2 + 3*r^2))/12}}*)

But how do this with half cylinder? enter image description here

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2
  • $\begingroup$ Replace body with DiscretizeRegion[Cylinder[], {{0, 1}, {-1, 1}, {-1, 1}}] $\endgroup$
    – N.J.Evans
    Commented Jan 11, 2021 at 15:51
  • 2
    $\begingroup$ @N.J.Evans.Yes works ,but I what solutions with:l,m ,r ? $\endgroup$
    – Mariusz Iwaniuk
    Commented Jan 11, 2021 at 15:54

1 Answer 1

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6
$\begingroup$

Takes a few seconds, but ImplicitRegion works:

body = ImplicitRegion[
  y^2 + z^2 <= r^2 && z >= 0 && -L/2 <= x <= L/2, {x, y, z}]
(ℐ = ρ MomentOfInertia[body, 
     Assumptions -> L > 0 && r > 0]) // MatrixForm
m Cancel[ℐ/(ρ Volume[body, 
       Assumptions -> r > 0 && L > 0])] // MatrixForm
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3
  • 3
    $\begingroup$ The representation body = RegionIntersection[Cylinder[{{-L/2, 0, 0}, {L/2, 0, 0}}, r], HalfSpace[{0, 0, -1}, {0, 0, 0}]] also works. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Jan 11, 2021 at 16:21
  • 1
    $\begingroup$ @J.M.'sennui I tried that, but the integral didn't finish. Maybe I didn't wait long enough. $\endgroup$
    – Michael E2
    Commented Jan 11, 2021 at 16:22
  • 5
    $\begingroup$ @J.M.'sennui OK, it doesn't take longer than it takes to go get a cup of coffee. :) $\endgroup$
    – Michael E2
    Commented Jan 11, 2021 at 16:29

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