Allgemein

>    T:=1/2*m*l^2*q1_t^2+q2_t^2;
V:=mg*l*(q1^2 +q2);
L:=T-V;

T := 1/2*l^2*q1_t^2+q2_t^2

V := mg*l*(q1^2+q2)

L := 1/2*l^2*q1_t^2+q2_t^2-mg*l*(q1^2+q2)

>    EulerLagr1:=diff(subs({q1=q1(t),q1_t=diff(q1(t),t),q2=q2(t),q2_t=diff(q2(t),t)},diff(L,q1_t)),t) - subs({q1=q1(t),q1_t=diff(q1(t),t),q2=q2(t),q2_t=diff(q2(t),t)},diff(L,q1))=0;
EulerLagr2:=diff(subs({q1=q1(t),q1_t=diff(q1(t),t),q2=q2(t),q2_t=diff(q2(t),t)},diff(L,q2_t)),t) - subs({q1=q1(t),q1_t=diff(q1(t),t),q2=q2(t),q2_t=diff(q2(t),t)},diff(L,q2))=0;

EulerLagr1 := l^2*diff(q1(t),`$`(t,2))+2*mg*l*q1(t) = 0

EulerLagr2 := 2*diff(q2(t),`$`(t,2))+mg*l = 0

>    A_q1:=2:
A_v1:=1:
A_q2:=1:
A_v2:=0:
dsolve({EulerLagr1,EulerLagr2,q1(0)=A_q1,D(q1)(0)=A_v1,q2(0)=A_q2,D(q2)(0)=A_v2});

>