# analytical dynamics 2 projects

Anonymous
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Question description

DEADLINE IS STRICT 46 HRS FROM NOW , EVEN AN HR MORE , I WILL NOT BE ABLE TO PAYUSE OF MATLAB IS MUST

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references2.jpeg
Please i need you to make to project , one for me and one for my friend... A paper that includes an equation of motion U might look for a crane or pendulum or any other applications that includes equations of motion? We have to solve it in Maple or Matlab (very important) Also you have to analyze and make sure that his work is correct or not ... These are some references you can look at them to find such a papers Please see the attached other two files

Ace_Tutor
School: Boston College

sorry for the late, attached is my answer

The MATLAB code for crane is shown below:
function [input]= Crane(n,count1,begin,the_final,
d_A,d_B,theta_epsilon_final,nominaleps)
syms epsilon;
R = zeros(2*count1+2,2*count1+2);
r = zeros(2*count1+2,1);
INI = simplify(d_A^(2*count1+2));
steps = (2*count1+2)^2;
step = 0;
h = waitbar(0,'input calculated');
for j = 1:2*count1+2
f = simplify(d_A^(j-1)*d_B);
s=0;
for i = 1:count1
for m = 1:n-s
R(s+2*(i-1)+m,j) = real(1/factorial(i1)*subs(f(m+s),epsilon,nominaleps));
step = step+1;
waitbar(step/steps)
end
f=simplify(diff(f, sym('epsilon'), 1));
s=2;
end
end
s = 0;
for i=1:count1
ini = -(1/factorial(i-1))*subs(diff(INI* begin ', sym('epsilon'), (i1)),epsilon,nominaleps);
for count = 1:n-s
r(s+2*(i-1)+ count) = ini(count +s);
end
s = 2;
end
close(h)
for count = 1:n
r(count) = r(count)+ the_final(count);
end
if count1>1
r(5) = r(5)+theta_epsilon_final;
end
input = flipud(R\r);
end

The math equations for crane is shown below:

According to the above analysis, it can be verified that the above solution is correct.

The MATLAB code for pendulum is shown below:
g = 9.8;
l = 5;
ini_angle1 = pi/3;
ini_angle2 = 0;
pend_x = 0;
pend_y = l;
fprintf('simulation')
choice = input('1 = phase portrait; 2 = time serie');
iterations = 1;
time_pause = 0.2;
run = 40;
tx = 0;
deq1=@(t,x) [x(2); -g/l * sin(x(1))];
[t,sol] = ode45(deq1,[0 run],[ini_angle1 ini_angle2]);
s1 = sol(:,1)';
s2 = sol(:,2)';
arraysize = size(t);
timestep = t(run) - t(run-1);
Cx = l*sin(s1);
Cy = l*cos(s2);
for i = 1 : max(arraysize)
subplot(2,1,1)
plotx = [pend_x Cx(iters)];
ploty = [pend_y Cy(iters)];
plot(Cx(iters),Cy(iters),'ko',plotx,ploty,'r-')
title(['pendulum \theta = ' num2str(s1(iters))],'fontsize',15)
xlabel('x [m]','fontsize',15)
ylabel('y [m]','fontsize',15)
axis([min(Cx) max(Cx) min(Cy) max(Cy)])
subplot(3,2,3)
if choice == 1
plot(s1(iters),s2(iters),'bo')
hold on
title(' phase portrait','fontsize',15)
xlabel('\alpha1','fontsize',12)
ylabel('\alpha2','fontsize',12)
axis([min(s1) max(s1) min(s2) max(s2)])
elseif choice == 2
plot(t(iters),s1(iters),'bo')
title([' time series \alpha1 t = ' num2str(t(iters))],'fontsize',15)
xlabel('t [seconds]','fontsize',15)
ylabel('\alpha1...

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Anonymous
Wow this is really good.... didn't expect it. Sweet!!!!

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