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Salinon

Definition

Defining inequalities

x^2 + y^2<=R^2 and y>=0 and (1/2 (-r - R) + x)^2 + y^2>=1/4 (R - r)^2 and ((r + R)/2 + x)^2 + y^2>=1/4 (R - r)^2 or x^2 + y^2<=r^2

Lamina properties

0<r<R

A = 1/4 π (r + R)^2

x^_ = (0, -(2 (r - R))/π)

Mechanical properties

J_x invisible comma x = 1/64 π (r + R)^2 (7 r^2 - 10 r R + 7 R^2)

J_y invisible comma y = 1/64 π (r + R)^2 (3 r^2 - 2 r R + 3 R^2)

J_zz = 1/32 π (r + R)^2 (5 r^2 - 6 r R + 5 R^2)

J_x invisible comma y = 0

r_x = 1/4 sqrt(7 r^2 - 10 r R + 7 R^2)
r_y = 1/4 sqrt(3 r^2 - 2 r R + 3 R^2)

Distance properties

p = 2 π R

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