% Problem 14.10

% Set up problem
digits 3
degrees on
frames n % n1> to the right, n2> upward, and n3> = n1> x n2>
points o,a,b % o is midpoint of pin, a is cable attachment point on beam
% b is cable attachment point in room
constants l{7},g,k
bodies c
mass c=m
variables q

% Rotation matrices
simprot(n,c,-3,q)

% Position vectors
p_o_co>=(l1/2-l7)*c1>+(l3/2-l6)*c2>
p_o_a>=(l1-l7)*c1>+(l3-l6)*c2>-l2/2*c3>
p_o_b>=(l1-l7)*n1>+(l5-l6)*n2>-(l2/2+l4)*n3>
p_a_b>=p_o_b>-p_o_a>
u_a_b>=unitvec(p_a_b>)

% Forces
force_co>=-m*g*n2>
l0=(l4^2+(l5-l3)^2)^0.5
force_a>=k*(mag(p_a_b>)-l0)*u_a_b>

% Moment about point O
m_o>=cross(p_o_co>,force_co>)+cross(p_o_a>,force_a>)
zero[1]=dot(m_o>,n3>)
stretch=mag(p_a_b>)-l0

evaluate(zero[1],q=4.417504472246025,l1=1.5,l2=0.15,l3=0.5,l4=1.0,l5=2.5,l6=0.15,l7=0.2,m=200,k=10000,g=9.8)
evaluate(stretch,q=4.417504472246025,l1=1.5,l2=0.15,l3=0.5,l4=1.0,l5=2.5,l6=0.15,l7=0.2,m=200,k=10000,g=9.8)
pause

% Output nonlinear equation solver
input l1=1.5,l2=0.15,l3=0.5,l4=1.0,l5=2.5,l6=0.15,l7=0.2,m=200,k=10000,g=9.8
units g=n/kg,k=n/m,m=kg,[l{1:7}]=m,q=deg
output stretch
code nonlinear(zero,q) prob14p10.m