I need to derive equations of motion using Lagrange' s method. I have xi, yi: i=0,1,2 coordinates with respect to phi(t), q1(t), q2(t), which are angles. When I have e.g. x_0 as a function of above mentioned coordinates, I differentiate it with respect to time t, then I calculate the energy I need to apply to EL equations and then, having: L=T-V when I need to differentiate dL/d(phi'(t)) using: diff(L,diff(phi(t),t)) I constantly get a messaege: ' Arguments, except for the first, must not be symbolic functions.' which appears only after I want to differentiate above L with respect to phi'(t). If I do not place the L differentiation, everything is okay. I changed the code so that I have phi(t) and dtPhi(t) which are both syms, but it does not solve the problem, I need to differentiate phi(t) w.r.t. t and then L w.r.t phi'(t). Summing up, I need to differentiate Function L with respect to phi'(t) and in 'syms' I only placed phi(t). Is it because in the second differentiation MATLAB uses diff(phi,t) as a function?
I have sth like this:
syms fi(t) q1(t) q2(t) l0 l1 l2 b0 b1 b2 m0 m1 m2 M i0 i1 i2 dtfi(t) dtq1(t) dtq2(t)
x0(t)=sin(fi)*(b1*sin(q1)+b0)*m1/M+(l1*sin(q1)+b2*sin(q1+q2)+b0)*m2/M-cos(fi)*(b1*cos(q1)+l0)*m1/M+(l1*cos(q1)+l0+b2*cos(q1+q2))*m2/M;
dt_x0=diff(x0,1);
y0(t)=-cos(fi)*(b1*sin(q1)+b0)*m1/M+(l1*sin(q1)+b2*sin(q1+q2)+b0)*m2/M-sin(fi)*(b1*cos(q1)+l0)*m1/M+(l1*cos(q1)+l0+b2*cos(q1+q2))*m2/M;
dt_y0=diff(y0,1);
x1(t)=cos(fi)*((b1*cos(q1)+l0)*(1-m1/M)-(l1*cos(q1)+b2*cos(q1+q2)+l0)*m2/M)-sin(fi)*((b1*sin(q1)+b0)*(1-m1/M)-(l1*sin(q1)+b0+b2*sin(q1+q2))*m2/M);
dt_x1=diff(x1,1);
y1(t)=sin(fi)*((b1*cos(q1)+l0)*(1-m1/M)-(l1*cos(q1)+b2*cos(q1+q2)+l0)*m2/M)+cos(fi)*((b1*sin(q1)+b0)*(1-m1/M)-(l1*sin(q1)+b0+b2*sin(q1+q2))*m2/M);
dt_y1=diff(y1,1);
x2(t)=cos(fi)*(l1*cos(q1)+b2*cos(q1+q2)+l0)-m1/M*(b1*cos(q1)+l0)-cos(fi)*(l1*cos(q1)+b2*cos(q1+q2)+l0)*m2/M-sin(fi)*(l1*sin(q1)+b0+b2*sin(q1+q2)-m1/M*(b1*sin(q1)+b0))-sin(fi)*(l1*sin(q1)+b2*sin(q1+q2)+b0)*m2/M;
dt_x2=diff(x2,1);
y2(t)=sin(fi)*(l1*cos(q1)+b2*cos(q1+q2)+l0)-m1/M*(b1*cos(q1)+l0)-sin(fi)*(l1*cos(q1)+b2*cos(q1+q2)+l0)*m2/M+cos(fi)*(l1*sin(q1)+b0+b2*sin(q1+q2)-m1/M*(b1*sin(q1)+b0))-cos(fi)*(l1*sin(q1)+b2*sin(q1+q2)+b0)*m2/M;
dt_y2=diff(y2,1);
dt_fi=diff(fi,1);
%dt_fi=diff(fi,t);
%Kinetic energy and also L=T-V, when V==0
L=1/2*m0*(diff(x0,1)^2+diff(y0,1)^2)+1/2*(i0+m0*(x0(t)^2+y0(t)^2))*diff(fi,1)^2+1/2*m1*(diff(x1,1)^2+diff(y1,1)^2)+1/2*(i1+m1*(x1(t)^2+y1(t)^2))*(diff(fi,1)+diff(q1,1))^2+1/2*m2*(diff(x2,1)^2+diff(y2,1)^2)+1/2*(i2+m2*(x2(t)^2+y2(t)^2))*(diff(fi,1)+diff(q1,1)+diff(q2,1))^2;
% Angular momentum
K=m0*(x0*diff(y0,1)-y0*diff(x0,1))+i0*diff(fi,1)+m1*(x1*diff(y1,1)-y1*diff(x1,1))+i1*(diff(fi,1)+diff(q1,1))+m2*(x2*diff(y2,1)-y2*diff(x2,1))+i2*(diff(fi,1)+diff(q1,1)+diff(q2,1));
%Lagrange II
%d/dt(dL/dq*_i)-dL/dq_i=0
%q_i: fi, q1, q2
%q*_i:dt_fi, dt_q1, dt_q2
%L=T-V=T
D11=diff(L, diff(fi,t)); %Here' s the problem, an error occurs; I need sth to differentiate it with respect to diff(fi,t)
D12=diff(D11,t);
D13=functionalDerivative(L, fi);
