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

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Tasks : Calculus - Multivariate : Integration : Center of Mass : Task/CenterOfMass3DSpherical

Center of Mass for 3D Region in Spherical Coordinates

Description

 

Determine ρ&conjugate0;,φ&conjugate0;, and θ&conjugate0;, the center of mass coordinates for a 3D region in spherical coordinates.

 

Center of Mass for 3D Region in Spherical Coordinates

(φ is the colatitude, measured down from the z-axis)

Density:

ρ

ρ

(1)

Region: ρ1φ,θρρ2φ,θ,φ1θφφ2θ,aθb

ρ1φ,θ

0

0

(2)

ρ2φ,θ

1

1

(3)

φ1θ

0

0

(4)

φ2θ

π6

16π

(5)

a

0

0

(6)

b

2 π

2π

(7)

Moments ÷ Mass:

Inert Integral - dρ dφ dθ

StudentMultivariateCalculusCenterOfMass,ρ=..,φ=..,θ=..,coordinates=sphericalρ,φ,θ,output=integral

∫02π∫016π∫01sinφ2cosθρ4ⅆρⅆφⅆθ∫02π∫016π∫01ρ3sinφⅆρⅆφⅆθ,∫02π∫016π∫01sinφ2sinθρ4ⅆρⅆφⅆθ∫02π∫016π∫01ρ3sinφⅆρⅆφⅆθ,∫02π∫016π∫01cosφρ4sinφⅆρⅆφⅆθ∫02π∫016π∫01ρ3sinφⅆρⅆφⅆθ

(8)

Explicit values for ρ&conjugate0;,φ&conjugate0;, and θ&conjugate0;, the center of mass given in spherical coordinates:

StudentMultivariateCalculusCenterOfMass,ρ=..,φ=..,θ=..,coordinates=sphericalρ,φ,θ

120π12π143π,0,0

(9)

Commands Used

Student[MultivariateCalculus][CenterOfMass]

Related Task Templates

Multivariate Calculus > Multiple Integration > Spherical

See Also

Student[MultivariateCalculus, Student[MultivariateCalculus][MultiInt]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam