problem with ode45 solving

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Juan Hurtado 2021-4-28

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评论： Star Strider 2021-5-3

采纳的回答： Star Strider

Hello, I'm trying to solve the following system of differential equations but I'm not getting the right answer

ode1 = diff(x) == v;

ode2 = diff(v) == u;

t_interval = [0,10]

x0 = 0

v0 = 0

u = 1

because of how things are set up I can wrap my head on creating the function. Any help would be appreciate it.

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Star Strider 2021-4-28

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Assuming both functions are functions of time —

syms x(t) v(t)

u = sym(1);

ode1 = diff(x) == v

ode1(t) =

ode2 = diff(v) == u

ode2(t) =

[x(t),v(t)] = dsolve(ode1,ode2, x(0)==0, v(0)==0)

x(t) =

v(t) =

figure

fplot(x, [0 10])

hold on

fplot(v, [0 1])

hold off

grid

xlabel('t')

legend('x(t)','v(t)')

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Star Strider 2021-5-3

在 MATLAB Online 中打开

Thank you!

This was a bit of a challenge, because of the way the Symbolic Math Toolbox works. The solution was to create a new copy of ‘v(t)’ in each iteratioon (as well as rename vector ‘x’ as ‘xv’ since ‘x’ is already defined as ‘x(t)’ and defining it as a vector later that confuses things).

syms x(t) v(t) x0

u = sym(1);

%time interval and initial conditions

xv = [-3, -2, -1, 1, 2, 3];

v0 = 0;

t_interval = [0,5];

%solution

ode1 = diff(x) == v;

ode2 = diff(v) == u;

[x(t),v(t)] = dsolve(ode1,ode2, x(0)==x0, v(0)==v0)

x(t) =

v(t) =

vx(t) = v % Copy 'v' to 'vx'

vx(t) =

for i = 1:length(xv)

v = vx % Create New Copy Of 'v' In Each Loop

ic_v = xv(i) % Display 'xv(i)'

v = subs(v,{x0},{ic_v}) % Substitute 'v(i)' For 'x0'

figure

fplot(x, t_interval)

hold on

fplot(v, t_interval)

hold off

grid

ylim([-3 16])

xlabel('t')

legend('x(t)','v(t)', 'Location','best')

end

v(t) =

ic_v = -3

v(t) =

ic_v = -2

v(t) =

ic_v = -1

v(t) =

ic_v = 1

v(t) =

ic_v = 2

v(t) =

ic_v = 3

v(t) =

Juan Hurtado 2021-5-3

This is great! Thank you. I was trying to do the same with the sign function part:

syms x(t) v(t) Y

u1 = sym(-sign(x));

%time interval and initial conditions

xv = [-3, -2, -1, 1, 2, 3];

v0 = 0;

t_interval = [0,20];

%solution

ode1 = diff(x) == v;

ode2 = diff(v) == u1;

[VF,Subs] = odeToVectorField(ode1,ode2);

[x(t),v(t)] = dsolve(ode1,ode2, x(0)==x0, v(0)==v0);

odefcn = matlabFunction(VF, 'Vars',{t,Y});

[t,y] = ode45(odefcn, t_interval, [x0 v0]+1E-8);

vx(t) = v; % Copy 'v' to 'vx'

figure

hold on

for i = 1:length(xv)

v = vx; % Create New Copy Of 'v' In Each Loop

ic_v = xv(i); % Display 'xv(i)'

v = subs(v,{x0},{ic_v}); % Substitute 'v(i)' For 'x0'

fplot(x, t_interval,'-k','LineWidth',1.2)

fplot(v, t_interval)

end

hold off

grid

xlabel('t')

icv = compose('v(t) x0 = %2d',xv);

legend(['x(t)',icv], 'Location','best')

and I get Unrecognized function or variable 'x0'. Which makes sense since now x0 is now a vector xv but I'm kind of confused on how to reeplace x0 for each of the elements in xv.