Why am I receiving an error for "odeToVectorField" when I am trying to convert second order differential equations to 1st order differential equations?

I have these three differential equations that I need to convert to first order, except the code errored and I recieved the following:

"Unable to convert the initial value problem to an equivalent dynamical system. Either the differential equations cannot be solved for the highest derivatives or inappropriate

Error in mupadengine/evalin_internal

Error in mupadengine/fevalHelper

Error in mupadengine/feval_internal

Error in odeToVectorField>mupadOdeToVectorField (line 171)

T = feval_internal(symengine,'symobj::odeToVectorField',sys,x,stringInput);

Error in odeToVectorField (line 119)

sol = mupadOdeToVectorField(varargin);

Error in DoubleIP_math (line 20)

V = odeToVectorField(eqn1_5,eqn1_4,eqn1_3)"

eqn1_5 = (m0 + m1 + m2)*diff(x,2) + (m1*l1 + m2*L2)*cos(theta1)*diff(theta1,2) + m2*l2*cos(theta2)*diff(theta2,2) - (m1*l1 + m2*L1)*sin(theta1)*(diff(theta1,1))^2 - m2*l2*sin(theta2)*(diff(theta2,1))^2 == u(t);

Unrecognized function or variable 'm0'.

% eqn1_5_f = odeToVectorField(eqn1_5)
eqn1_4 = (m1*(l1)^2 + m2*(L1)^2 + I1)*diff(theta1,2) + (m1*l1 + m2*L1)*cos(theta1)*diff(x,2) + m2*L1*l2*cos(theta1-theta2)*diff(theta2,2) + m2*L1*l2*sin(theta1-theta2)*(diff(theta2,1))^2 - g*(m1*l1 + m2*L1)*sin(theta1) == 0;
% eqn1_4_f = odeToVectorField(eqn1_4)
eqn1_3 = m2*l2*cos(theta2)*diff(x,2) + m2*L1*l2*cos(theta1-theta2)*diff(theta1,2) + (m2*(l2)^2 + I2)*diff(theta2,2) - m2*L1*l2*sin(theta1-theta2)*(diff(theta1,1))^2 - m2*g*l2*sin(theta2) == 0;
% eqn1_3_f = odeToVectorField(eqn1_3)
V = odeToVectorField(eqn1_5 ,eqn1_4, eqn1_3)

[Akekaphop Kesavadhana]

I already have defined the variables to be symbolic and the issue persisted. Any other ideas?

% syms m0 m1 m2 l1 l2 L1 L2 I1 I2 g u(t) x(t) theta1 theta2

Answer 1

[Sam Chak]

Hi @Akekaphop Kesavadhana

Previously, theta1 and theta2 were created as scalar variables when they should be functions of time.

% syms m0 m1 m2 l1 l2 L1 L2 I1 I2 g u(t) x(t) theta1 theta2 
%                                              ^^^^   ^^^^
  syms m0 m1 m2 l1 l2 L1 L2 I1 I2 g u(t) x(t) theta1(t) theta2(t)

eqn1_5 = (m0 + m1 + m2)*diff(x,2) + (m1*l1 + m2*L2)*cos(theta1)*diff(theta1,2) + m2*l2*cos(theta2)*diff(theta2,2) - (m1*l1 + m2*L1)*sin(theta1)*(diff(theta1,1))^2 - m2*l2*sin(theta2)*(diff(theta2,1))^2 == u(t);
eqn1_4 = (m1*(l1)^2 + m2*(L1)^2 + I1)*diff(theta1,2) + (m1*l1 + m2*L1)*cos(theta1)*diff(x,2) + m2*L1*l2*cos(theta1-theta2)*diff(theta2,2) + m2*L1*l2*sin(theta1-theta2)*(diff(theta2,1))^2 - g*(m1*l1 + m2*L1)*sin(theta1) == 0;
eqn1_3 = m2*l2*cos(theta2)*diff(x,2) + m2*L1*l2*cos(theta1-theta2)*diff(theta1,2) + (m2*(l2)^2 + I2)*diff(theta2,2) - m2*L1*l2*sin(theta1-theta2)*(diff(theta1,1))^2 - m2*g*l2*sin(theta2) == 0;
[V, S] = odeToVectorField(eqn1_5 ,eqn1_4, eqn1_3)

V = 

S = 

[Akekaphop Kesavadhana]

Thank you so much, it seemed like it has worked!