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    Rhombus

    Defining inequalities

    cos(θ) (a sin(θ) + y) + x sin(θ)>=0 and cos(θ) (a sin(θ) + y)>=x sin(θ) and a sin(θ) cos(θ)>=x sin(θ) + y cos(θ) and sin(θ) (a cos(θ) + x)>=y cos(θ)

    Definition

    Alternate names

    diamond | equilateral parallelogram | rhomb

    Lamina properties

    (-cos(θ) a, 0) | (0, -sin(θ) a) | (cos(θ) a, 0) | (0, sin(θ) a)

    4

    a>0 and 0<θ<π/2

    2 a cos(θ) | 2 a sin(θ)

    A = a^2 sin(2 θ)

    x^_ = (0, 0)

    Mechanical properties

    J_x invisible comma x = 1/3 a^4 sin^3(θ) cos(θ)

    J_y invisible comma y = 1/3 a^4 sin(θ) cos^3(θ)

    J_zz = 1/6 a^4 sin(2 θ)

    J_x invisible comma y = 0

    r_x = (a sin(θ))/sqrt(6) r_y = (a cos(θ))/sqrt(6)

    Distance properties

    a | a | a | a

    p = 4 a

    r = a sin(θ) cos(θ)

    2 a max(cos(θ), sin(θ))

    χ = 1

    Classes

    convex laminae | equilateral polygonal laminae | polygonal laminae | quadrilateral laminae

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