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    Square

    Defining inequalities

    -a/2<=x<=a/2 and -a/2<=y<=a/2

    Definition

    Lamina properties

    (-a/2, -a/2) | (a/2, -a/2) | (a/2, a/2) | (-a/2, a/2)

    4

    a>0

    sqrt(2) a | sqrt(2) a

    r = a/2

    h = 1/2 (sqrt(2) - 1) a

    a

    A = a^2

    x^_ = (0, 0)

    Mechanical properties

    J_x invisible comma x = a^4/12

    J_y invisible comma y = a^4/12

    J_zz = a^4/6

    J_x invisible comma y = 0

    r_x = a/(2 sqrt(3)) r_y = a/(2 sqrt(3))

    K = 1/3 a^4 (1 - (192 sum_(n=1)^∞ tanh(1/2 π (2 n - 1))/(2 n - 1)^5)/π^5)

    Distance properties

    a | a | a | a

    p = 4 a

    r = a/2

    R = a/sqrt(2)

    sqrt(2) a

    χ = 1

    s^_ = 1/15 a (2 + sqrt(2) + 5 sinh^(-1)(1))

    A^_ = (11 a^2)/144

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