Modified limits of integral for a sphere

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I have a sphere that floating at the air-water interface like the picture.

sphere

It has 2 parts P and S. When the sphere rotates, area of P and S portion change as a function of rotation. The calculation shows the Area of P side at the air denoted by A(p-a).

equation

Can someone explain how the limits of integrals defined for this case? I know the limits for spherical coordinates but did not get for this specific case where only a portion of sphere need to take into account.

edited Jul 18 at 5:44

Parcly Taxel

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asked Jul 18 at 5:35

Tanvir

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up vote
0
down vote

favorite

I have a sphere that floating at the air-water interface like the picture.

sphere

It has 2 parts P and S. When the sphere rotates, area of P and S portion change as a function of rotation. The calculation shows the Area of P side at the air denoted by A(p-a).

equation

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

asked Jul 18 at 5:35

Tanvir

add a commentÂ |Â

up vote
0
down vote

favorite

I have a sphere that floating at the air-water interface like the picture.

sphere

It has 2 parts P and S. When the sphere rotates, area of P and S portion change as a function of rotation. The calculation shows the Area of P side at the air denoted by A(p-a).

equation

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

asked Jul 18 at 5:35

Tanvir

I have a sphere that floating at the air-water interface like the picture.

sphere

It has 2 parts P and S. When the sphere rotates, area of P and S portion change as a function of rotation. The calculation shows the Area of P side at the air denoted by A(p-a).

equation

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

asked Jul 18 at 5:35

Tanvir

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

edited Jul 18 at 5:44

Parcly Taxel

33.6k136588

asked Jul 18 at 5:35

Tanvir

asked Jul 18 at 5:35

Tanvir

asked Jul 18 at 5:35

Tanvir

add a commentÂ |Â

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