2nd order differential equations

For a Project I got to solve these Lagrange equations!

sdolve does not work

I tried formulating 2 equations of first order instead of one equation of second order, but this does not work either. Because there is no explicit solution. Start values would be: phi(0)==0.9424, phi_dot(0)==0

any ideas?

clear
Parameter
    m= 100;
    c= 3588;
    g= 9.81;
    
syms phi(t) m c g 
    alpha=sin((1.7-2.1*cos(phi(t)))/3.6);
    r1=((-2.1*sin(phi(t))+1.8*cos(alpha))^2+(2.1*cos(phi(t))+1.8*sin(alpha))^2)^0.5;
    r1_d=diff(r1);

alpha_d=diff(alpha);

Energie
U=1/2*c*(1.8^2+0.6^2-2*1.8*0.6*cos(phi(t)));
W=m*g*(2.1*cos(phi(t))+1.8*sin(alpha));
V=U+W

T_trans=0.5*m*r1_d^2;
T_rot=1/3*m*3.6^2*alpha_d^2;
T=T_trans+T_rot

Lagrange
T_dv=diff(T,diff(phi(t)));

L_1=diff(T_dv,t);

L_2=diff(T,phi(t));

L_3=diff(V,phi(t));

F=L_1-L_2+L_3
F_s=simplify(F)

F_ss=solve(F_s,diff(phi(t), t, 2))

[Torsten]

any ideas?

Use "matlabFunction" to create a function handle for your differential equation(s)

matlabFunction(F)

and use "ode15i" to solve the equations numerically.

[Patrick Nowohradsky]

Like this?

Lagrange
T_dv=diff(T,diff(phi(t)));

L_1=diff(T_dv,t);

L_2=diff(T,phi(t));

L_3=diff(V,phi(t));

F=L_1-L_2+L_3;
F_s=simplify(F)
F_ss=matlabFunction(F_s);
phi0 = 0.9424;
phid0 = 0;
tspan=[0 30];
[t,y]=ode15i(F_ss,tspan,phi0,phid0)

figure
t_t=linspace(0,2*pi);
plot(t, y)

Then I get: Warning: Function 'phi' not verified to be a valid MATLAB function

[Ganesh Gudipati]

Since you didn't initialize the variable phi, MATLAB would be searching if there exists a function 'phi'.

Firstly, intialize the value of phi and procced. This should resolve your error.