MATLAB program: plotting differential equation

Question

Andy.P 2021-11-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1598079-matlab-program-plotting-differential-equation

编辑： Andy.P 2021-12-1

Compute the new velocity and acceleration of the aircraft after a change in power level. During a test flight, the test pilot has set the engine power at 50,000 Newtons, which causes the 20,000 Kg aircraft to attend a cruise speed of 250 m/s. The engine throttles are then set to a power level at 80,000 Newtons, and then the aircraft begins to accelerate. The differential equation that determines the acceleration of the aircraft is dv/dt = a(v,t) = T/m - 0.00005v^2

T = thrust level in Newtons (80,000 Newtons)

m = mass in Kg (20,000 Kg)

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Steven Lord 2021-11-29

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Image Analyst 2021-11-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1598079-matlab-program-plotting-differential-equation#answer_843034

编辑：Image Analyst 2021-11-29

Here's a start

T1 = 50000; % Initial thrust.

T2 = 80000; % Second thrust.

m = 20000;

v1 = 250; % Initial velocity.

% Note v2 = v1 + a * t, and a(t) = T2/m - 0.00005v(t)^2 (the stated formula)

v2 = v1;

for t = 2 : 40

a = T2/m - 0.00005 * v2(t-1)^2;

v2(t) = v2(t-1) + a * t;

end

plot(v2, 'b-', 'LineWidth', 2)

grid on;

xlabel('Time')

ylabel('Velocity')

2 个评论
显示无隐藏无

Andy.P 2021-11-30

编辑：Andy.P 2021-11-30

Great and how come you did * v2 ( t -1 ) ^ 2. Why t - 1 ?

Also do you integrate dv/dt ?

Image Analyst 2021-11-30

Let's say that you have the last (past) time point, and you have a (future/next) time point that you want to compute. The acceleration cannot depend on the next velocity value -- you don't know that velocity yet! So you have to compute the acceleration based on the only velocity you know, which is the last velocity.

I didn't do any integration or differentiation. It was just strictly digital algebra. If you want/need to integrate some curve you can use trapz(), sum(), or maybe integrate().

请先登录，再进行评论。