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Paralelogramo

Definition

Defining inequalities

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

Lamina properties

(0, 0) | (b, 0) | (cos(A) a + b, sin(A) a) | (cos(A) a, sin(A) a)

4

a>0 and b>0 and 0<A<π

sqrt(a^2 - 2 a b cos(A) + b^2) | sqrt(a^2 + 2 a b cos(A) + b^2)

a sin(A)

A = a b sin(A)

x^_ = (1/2 (cos(A) a + b), 1/2 sin(A) a)

Mechanical properties

J_x invisible comma x = 1/3 a^3 b sin^3(A)

J_y invisible comma y = 1/6 a b sin(A) (a^2 cos(2 A) + a^2 + 3 a b cos(A) + 2 b^2)

J_zz = 1/6 a b sin(A) (2 (a^2 + b^2) + 3 a b cos(A))

J_x invisible comma y = -1/12 a^2 b sin^2(A) (4 a cos(A) + 3 b)

Distance properties

b | a | b | a

p = 2 (a + b)

max(sqrt(a^2 - 2 a b cos(A) + b^2), sqrt(a^2 + 2 a b cos(A) + b^2))

χ = 1

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