dx/dt=-a*sint,dy/dt=b*cost,ds=√((dx/dt)^2+(dy/dt)^2)dt=√(a^2*sint^2+b^2*cost^2)dt其质量=∫ρds=4∫(0,π/2)b*sint*√(a^2*sint^2+b^2*cost^2)dt=4∫(0,π/2)b*sint*√(a^2-(a^2-b^2)*cost^2)dt=4∫(0,π/2)b*sint*√(a^2-c^2*cost^2)dt=4∫(0,π/2)a*b*sint√(1-e^2*cost^2)dt=4a*b*∫(0,π/2)sint√(1-e^2*cost^2)dt=4a*b*[1/2*((1-e^2)^(1/2)*e+arcsin(e))/e]=2a*b*(b/a+1/e*arcsin(e))=2b*(b+a/e*arcsin(e))
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