%     File:  StaticSuspensionBridge.al
%  Problem:  Static equilibrium of suspension bridge
%--------------------------------------------------------------------
%       Reference frames, rigid bodies, points, and particles
NewtonianFrame  N    % Ground (Earth)
RigidBody  A, B      % Support towers
Point      AL(A)     % Highest  left-point of A
Point      AR(A)     % Highest right-point of A
Point      BL(B)     % Highest  left-point of B
Point      BR(B)     % Highest right-point of B
Point      CR        % Right-most point of cable C (where force is applied)
Particle   Q         % Particle modeling objects attached to cable between A and B
%--------------------------------------------------------------------
%       Constants (all constants are positive +)
Constant   dA+       % Distance between No and tower A (horizontal)
Constant   w+        % Width of towers (horizontal)
Constant   dB+       % Distance between tower A and tower B (horizontal)
Constant   h+        % Height of top of towers above No (vertical)
Constant   L3+       % Distance between point AR and particle Q
Constant   m+        % Mass of particle Q
Constant   g+        % Earth's local gravitational acceleration
%--------------------------------------------------------------------
%       Angles used for static analysis
Constant   theta     % Angle between Nx> and the line connecting AR to CR
Variable   q3        % Angle between Nx> and the connecting line AR to Q
%--------------------------------------------------------------------
%       Tension in various portions of the cable
Variable   T1        % Tension in cable between No and AL
Variable   T2        % Tension in cable between AL and AR
Variable   T3        % Tension in cable between AR and Q
Variable   T4        % Tension in cable between Q  and BL
Variable   T5        % Tension in cable between BL and BR
Constant   F         % Tension in cable between BR and CR (known)
%--------------------------------------------------------------------
%       Support forces from towers
Variable   ALy       % Vertical support force on cable from A at AL
Variable   ARy       % Vertical support force on cable from A at AR
Variable   BLy       % Vertical support force on cable from B at BL
Variable   BRy       % Vertical support force on cable from B at BR
%--------------------------------------------------------------------
%       Position vectors
AL.SetPosition( No, dA*Nx> + h*Ny> )
AR.SetPosition( AL,  w*Nx> )
Q.SetPosition(  AR,  L3*cos(q3)*Nx> - L3*sin(q3)*Ny> )
BL.SetPosition( AR,  dB*Nx> )
BR.SetPosition( BL,  w*Nx> )
%--------------------------------------------------------------------
%       Helpful lengths
L1 = AL.GetDistance( No )
L4 = BL.GetDistance( Q )
%--------------------------------------------------------------------
%       Helpful unit vectors
NoUnitVectorFromAL> = No.GetPosition( AL ) / L1
QUnitVectorFromAR>  =  Q.GetPosition( AR ) / L3
QUnitVectorFromBL>  =  Q.GetPosition( BL ) / L4
CRUnitVectorFromBR> = cos(theta)*Nx> - sin(theta)*Ny>
%--------------------------------------------------------------------
%       Sum of forces at various points in the cable
SumOfForcesInCableAtAL> =  T1*NoUnitVectorFromAL> + ALy*Ny> + T2*Nx>
SumOfForcesInCableAtAR> =  T3*QUnitVectorFromAR>  + ARy*Ny> - T2*Nx>
SumOfForcesInCableAtBL> =  T4*QUnitVectorFromBL>  + BLy*Ny> + T5*Nx>
SumOfForcesInCableAtBR> =   F*CRUnitVectorFromBR> + BRy*Ny> - T5*Nx>
SumOfForcesInCableAtQ>  = -T3*QUnitVectorFromAR>  - m*g*Ny> - T4*QUnitVectorFromBL>
%--------------------------------------------------------------------
%       Create scalar equations
Zero[1] = Dot( SumOfForcesInCableAtAL>, Nx> )
Zero[2] = Dot( SumOfForcesInCableAtAL>, Ny> )
Zero[3] = Dot( SumOfForcesInCableAtAR>, Nx> )
Zero[4] = Dot( SumOfForcesInCableAtAR>, Ny> )
Zero[5] = Dot( SumOfForcesInCableAtBL>, Nx> )
Zero[6] = Dot( SumOfForcesInCableAtBL>, Ny> )
Zero[7] = Dot( SumOfForcesInCableAtBR>, Nx> )
Zero[8] = Dot( SumOfForcesInCableAtBR>, Ny> )
Zero[9] = Dot( SumOfForcesInCableAtQ>,  Nx> )
Zero[10] =Dot( SumOfForcesInCableAtQ>,  Ny> )
%--------------------------------------------------------------------
%       Input values for constants
Input  dA=40 m, w=5 m, dB=100 m, h=30 m, L3=70 m
Input  m=100000 kg, g=9.8 m/sec^2
Input  F=700000 N, theta=20 deg           % (magnitude and direction)
%--------------------------------------------------------------------
%       Solve nonlinear equations for q3, T1, T2, T3, T4, T5, ALy, ARy, BLy, BRy
% Add your code here!