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    Circle-circle Intersection

    Definition

    Defining inequalities

    (x - d/2)^2 + y^2<=a^2 and (d/2 + x)^2 + y^2<=a^2

    Lamina properties

    0<d<2 a

    A = -1/2 d sqrt(4 a^2 - d^2) - 2 a^2 tan^(-1)(d/sqrt(4 a^2 - d^2)) + π a^2

    x^_ = (0, 0)

    Mechanical properties

    J_x invisible comma x = 1/48 (12 π a^4 - 10 a^2 d sqrt(4 a^2 - d^2) + d^3 sqrt(4 a^2 - d^2) - 24 a^4 tan^(-1)(d/sqrt(4 a^2 - d^2)))

    J_y invisible comma y = 1/48 (12 π a^4 + 2 a^2 d (6 π d - 13 sqrt(4 a^2 - d^2)) - 24 a^2 (a^2 + d^2) tan^(-1)(d/sqrt(4 a^2 - d^2)) - d^3 sqrt(4 a^2 - d^2))

    J_zz = 1/4 a^2 (-3 d sqrt(4 a^2 - d^2) - 2 (2 a^2 + d^2) tan^(-1)(d/sqrt(4 a^2 - d^2)) + 2 π a^2 + π d^2)

    J_x invisible comma y = 0

    Distance properties

    p = 4 a cos^(-1)(d/(2 a))

    sqrt(4 a^2 - d^2)

    χ = 1

    Classes

    convex laminae | curvilinear laminae

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