Plot the acceleration with ODE45

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Elnur Shahbalayev
Elnur Shahbalayev 2020-11-29
评论： Elnur Shahbalayev 2020-11-29
Hello, I have the problem to plot accelaration i matlab with ODE45 function.
Here is the question:
I wrote the function like this:
function dxdt = vdp1(t,x)
dxdt = [x(2); (9.8 - 0.00324*sign(x(2))*x(2)^2-(1/7)*(x(1)-150)*heaviside(x(1)-150))];
end
For part 1 and 2,to get results I wrote this code:
%Part 1
[t,x] = ode45(@vdp1,[0 11.47], [0;0])
plot(t,x(:,1),'-o',t,x(:,2),'-o')
title('Solution with ODE45');
xlabel('Time t');
ylabel('Solution x');
legend('x_1','x_2')
% Part 2
[t,x] = ode45(@vdp1,[0 5.988], [0;0])
plot(t,x(:,1),'-o',t,x(:,2),'-o')
title('Solution with ODE45');
xlabel('Time t');
ylabel('Solution x');
% legend('x_1','x_2')
[t,x] = ode45(@vdp1,[0 11.47], [0;0])
plot(t,x(:,1),'-o',t,x(:,2),'-o')
title('Solution with ODE45');
xlabel('Time t');
ylabel('Solution x');
legend('x_1','x_2')
Now, I don't know how to find accelaration with with this way. Please can anyone help me. Thanks in advance.

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回答（1 个）

James Tursa
James Tursa 2020-11-29
编辑：James Tursa 2020-11-29
You find acceleration by taking the x solution from ode45( ) and feeding that back into your derivative function vdp1( ). Since your derivative function is not vectorized, you will have to do this in a loop.
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James Tursa
James Tursa 2020-11-29
编辑：James Tursa 2020-11-29
E.g., something like this:
[t,x] = ode45(@vdp1,[0 11.47], [0;0]); % solve the ode
n = size(x,1); % figure out how many rows are in the solution
xdot = zeros(size(x)); % allocate the derivative matrix
for k=1:n % loop through each solution vector to fill in the derivative matrix
xdot(k,:) = vdp1(t(k),x(k,:)); % calculate the derivative at time t(k)
end
acceleration = xdot(:,2); % pick off the acceleration values

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