Center of Mass for 3D Region in Cartesian Coordinates - Maple Programming Help

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Center of Mass for 3D Region in Cartesian Coordinates

Description

 

Determine x&conjugate0;, y&conjugate0;, and z&conjugate0;, the center of mass coordinates for a 3D region in Cartesian coordinates.

 

Center of Mass for 3D Region in Cartesian Coordinates

Density:

x y z

xyz

(1)

Region: z1x,yzz2x,y,y1xyy2x,axb

z1x,y

1x y

1xy

(2)

z2x,y

10x2y2

10x2y2

(3)

y1x

x2

x2

(4)

y2x

x

x

(5)

a

0

0

(6)

b

1

1

(7)

Moments÷Mass:

Inert Integral - dz dy dx

StudentMultivariateCalculusCenterOfMass,z=.., y=..,x=..,output=integral

∫01∫x2x∫1xy10x2y2z2xyⅆzⅆyⅆx∫01∫x2x∫1xy10x2y2xyzⅆzⅆyⅆx,∫01∫x2x∫1xy10x2y2y2xzⅆzⅆyⅆx∫01∫x2x∫1xy10x2y2xyzⅆzⅆyⅆx,∫01∫x2x∫1xy10x2y2x2yzⅆzⅆyⅆx∫01∫x2x∫1xy10x2y2xyzⅆzⅆyⅆx

(8)

Explicit values for x&conjugate0;, y&conjugate0;, and z&conjugate0;

StudentMultivariateCalculusCenterOfMass,z=.., y=..,x=..

3507743573782,332885573782,24943173729583

(9)

Commands Used

Student[MultivariateCalculus][CenterOfMass]

Related Task Templates

Multivariate Calculus > Multiple Integration > Cartesian 3-D

See Also

Student[MultivariateCalculus], Student[MultivariateCalculus][MultiInt]


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