(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume a ball has mass "Me" and wrapped by water like ocean and earth ,the water has mass "Mw" and density [itex]\rho[/itex] ,when the ball spin with angular velocity [itex]\omega[/itex] ,and the shade of system goes to ellipsoid, please expres the water depth in spherical coordinate system

2. Relevant equations

3. The attempt at a solution

i was thinking to use calculus of variation to solve this problem , i assume radius of ball is "R" and shell to the water's surface is "a" , when ball spin , the new distant between shell and surface is "a+[itex]\eta[/itex] "

from lagrange equation L= T-V

L=[itex]\frac{1}{2}[/itex][itex]\rho[/itex][itex]\int[/itex][([itex]\frac{\partial\eta}{\partial t}[/itex])[itex]^{2}[/itex]+(a+[itex]\eta[/itex] )[itex]^{2}[/itex][itex]\omega[/itex] [itex]^{2}[/itex]]r[itex]^{2}[/itex]sin[itex]\theta[/itex]drd[itex]\theta[/itex]d[itex]\varphi[/itex]+GMe[itex]\rho[/itex] [itex]\int[/itex][itex]\frac{1}{r}[/itex]r[itex]^{2}[/itex]sin[itex]\theta[/itex]drd[itex]\theta[/itex]d[itex]\varphi[/itex]

am i right?

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# Homework Help: A question about classical dynamic

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