Trying to solve systems of ODEs and graph answer

1 vue (au cours des 30 derniers jours)
Cason Cox
Cason Cox le 30 Nov 2022
Trying to solve system of ODEs using other working code but getting error on line with "matlabFunction" I beleave the error has somethig to do with 'vars' but I can not figure out what. ODEs equation of motrions are correct and code works, error is just with graphing.
Original Code
clear;clc;
syms theta_1(t) theta_2(t) L_1 L_2 m_1 m_2 g
x_1 = L_1*sin(theta_1);
y_1 = -L_1*cos(theta_1);
x_2 = x_1 + L_2*sin(theta_2);
y_2 = y_1 - L_2*cos(theta_2);
vx_1 = diff(x_1);
vy_1 = diff(y_1);
vx_2 = diff(x_2);
vy_2 = diff(y_2);
ax_1 = diff(vx_1);
ay_1 = diff(vy_1);
ax_2 = diff(vx_2);
ay_2 = diff(vy_2);
syms T_1 T_2
eqx_1 = m_1*ax_1(t) == -T_1*sin(theta_1(t)) + T_2*sin(theta_2(t))
eqy_1 = m_1*ay_1(t) == T_1*cos(theta_1(t)) - T_2*cos(theta_2(t)) - m_1*g
eqx_2 = m_2*ax_2(t) == -T_2*sin(theta_2(t))
eqy_2 = m_2*ay_2(t) == T_2*cos(theta_2(t)) - m_2*g
Tension = solve([eqx_1 eqy_1],[T_1 T_2]);
eqRed_1 = subs(eqx_2,[T_1 T_2],[Tension.T_1 Tension.T_2]);
eqRed_2 = subs(eqy_2,[T_1 T_2],[Tension.T_1 Tension.T_2]);
L_1 = 1;
L_2 = 1.5;
m_1 = 2;
m_2 = 1;
g = 9.8;
eqn_1 = subs(eqRed_1)
eqn_2 = subs(eqRed_2)
[V,S] = odeToVectorField(eqn_1,eqn_2)
S
M = matlabFunction(V,'vars',{'t','Y'})
initCond = [pi/4 0 pi/6 0];
sols = ode45(M,[0 10],initCond);
plot(sols.x,sols.y)
legend('\theta_2','d\theta_2/dt','\theta_1','d\theta_1/dt')
title('Solutions of State Variables')
xlabel('Time (s)')
ylabel('Solutions (rad or rad/s)')
New codewith matlabFunction error
clear; clc;
% Initalize Variables
syms theta1(t) theta2(t) r1 r2 m1 m2 g
% Initalize Kinematic Constraints
x1 = r1*sin(theta1);
y1 = -r1*cos(theta1);
x2 = x1+r2*sin(theta2+theta1);
y2 = y1-r2*cos(theta2+theta1);
% Initalize Velocity Equations
x1dot=diff(x1);
y1dot=diff(y1);
x2dot=diff(x2);
y2dot=diff(y2);
% Solve for Potential Energy
pe=m1*g*y1+m2*g*y2;
%Solve for Kinetic Energy
ke=1/2*m1*(x1dot^2+y1dot^2)+1/2*m2*(x2dot^2+y2dot^2);
simplify(ke);
% Solve for L=KE-PE
l=ke-pe;
simplify(l);
% Initalize Variables
syms theta1dot theta2dot
% Solve for partial derivitive of L by theta1dot
eqn1=subs(diff(subs(l(t), diff(theta1(t)), theta1dot), theta1dot), theta1dot, diff(theta1(t)));
eqn1=simplify(eqn1);
% Solve for the time derivative of eqn1
eqn1=diff(eqn1);
eqn1=simplify(eqn1);
% Solve for partial derivitive of L by theta1
a=simplify(diff(l,theta1));
% Solve for first equation of motion
eqn1=simplify(eqn1-a)
% Solve for partial derivitive of L by theta2dot
eqn2=subs(diff(subs(l(t), diff(theta2(t)), theta2dot), theta2dot), theta2dot, diff(theta2(t)));
eqn2=simplify(eqn2);
% Solve for the time derivative of eqn2
eqn2=diff(eqn2);
eqn2=simplify(eqn2);
% Solve for partial derivitive of L by theta2
b=simplify(diff(l,theta2));
% Solve for second equation of motion
eqn2=simplify(eqn2-b)
r1 = 1;
r2 = 1.5;
m1 = 2;
m2 = 1;
g = 9.8;
[V,S] = odeToVectorField(eqn1,eqn2)
M = matlabFunction(V,'vars',{'t','Y'})
initCond = [pi/4 0 pi/6 0];
sols = ode45(M,[0 10],initCond);
plot(sols.x,sols.y)
legend('\theta_2','d\theta_2/dt','\theta_1','d\theta_1/dt')
title('Solutions of State Variables')
xlabel('Time (s)')
ylabel('Solutions (rad or rad/s)')

Réponses (1)

Walter Roberson
Walter Roberson le 1 Déc 2022
If you define a symbolic variable and use it in an expression, and later assign a numeric value to the same name, then that does not change the symbolic variable that is in the expression. The situation is much like how if you
A = 3
B = A*2 + 1
A = 9
then B does not suddenly change from 3*2+1 to instead evaluate to 9*2+1 . The value of A as of the time that B was defined is what is used in B, and changes to A after that do not affect B. The same is true for if it had been syms A instead of assigning a numeric value to A -- changing A afterwards would not change the place the symbolic version was already used.
% Initalize Variables
syms theta1(t) theta2(t) r1 r2 m1 m2 g
% Initalize Kinematic Constraints
x1 = r1*sin(theta1);
y1 = -r1*cos(theta1);
x2 = x1+r2*sin(theta2+theta1);
y2 = y1-r2*cos(theta2+theta1);
% Initalize Velocity Equations
x1dot=diff(x1);
y1dot=diff(y1);
x2dot=diff(x2);
y2dot=diff(y2);
% Solve for Potential Energy
pe=m1*g*y1+m2*g*y2;
%Solve for Kinetic Energy
ke=1/2*m1*(x1dot^2+y1dot^2)+1/2*m2*(x2dot^2+y2dot^2);
simplify(ke);
% Solve for L=KE-PE
l=ke-pe;
simplify(l);
% Initalize Variables
syms theta1dot theta2dot
% Solve for partial derivitive of L by theta1dot
eqn1=subs(diff(subs(l(t), diff(theta1(t)), theta1dot), theta1dot), theta1dot, diff(theta1(t)));
eqn1=simplify(eqn1);
% Solve for the time derivative of eqn1
eqn1=diff(eqn1);
eqn1=simplify(eqn1);
% Solve for partial derivitive of L by theta1
a=simplify(diff(l,theta1));
% Solve for first equation of motion
eqn1=simplify(eqn1-a)
eqn1(t) = 
% Solve for partial derivitive of L by theta2dot
eqn2=subs(diff(subs(l(t), diff(theta2(t)), theta2dot), theta2dot), theta2dot, diff(theta2(t)));
eqn2=simplify(eqn2);
% Solve for the time derivative of eqn2
eqn2=diff(eqn2);
eqn2=simplify(eqn2);
% Solve for partial derivitive of L by theta2
b=simplify(diff(l,theta2));
% Solve for second equation of motion
eqn2=simplify(eqn2-b)
eqn2(t) = 
r1 = 1;
r2 = 1.5;
m1 = 2;
m2 = 1;
g = 9.8;
[V,S] = odeToVectorField(subs(eqn1),subs(eqn2))
V = 
S = 
M = matlabFunction(V,'vars',{'t','Y'})
M = function_handle with value:
@(t,Y)[Y(2);(sin(Y(3)).*-2.94e+2+sin(Y(1)+Y(3)).*1.96e+2+sin(Y(1)).*Y(2).^2.*1.5e+1+sin(Y(1)).*Y(4).^2.*3.5e+1-cos(Y(1)).*sin(Y(3)).*1.96e+2+cos(Y(1)).*sin(Y(1)+Y(3)).*9.8e+1+cos(Y(1)).*sin(Y(1)).*Y(2).^2.*1.0e+1+cos(Y(1)).*sin(Y(1)).*Y(4).^2.*2.0e+1+sin(Y(1)).*Y(2).*Y(4).*3.0e+1+cos(Y(1)).*sin(Y(1)).*Y(2).*Y(4).*2.0e+1)./(cos(Y(1)).^2.*1.0e+1-3.0e+1);Y(4);((sin(Y(3)).*-2.94e+2+sin(Y(1)).*Y(2).^2.*1.5e+1+sin(Y(1)).*Y(4).^2.*1.5e+1+cos(Y(1)).*sin(Y(1)+Y(3)).*9.8e+1+cos(Y(1)).*sin(Y(1)).*Y(4).^2.*1.0e+1+sin(Y(1)).*Y(2).*Y(4).*3.0e+1).*(-1.0./1.0e+1))./(cos(Y(1)).^2-3.0)]
initCond = [pi/4 0 pi/6 0];
sols = ode45(M,[0 10],initCond);
plot(sols.x,sols.y)
legend('\theta_2','d\theta_2/dt','\theta_1','d\theta_1/dt')
title('Solutions of State Variables')
xlabel('Time (s)')
ylabel('Solutions (rad or rad/s)')

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