I have a rather complicated differential equation, $$\ddot \theta=\frac{ml(g-l\dot\theta^2 \cos \theta)(\sin\theta - \mu_k \cos\theta)}{I+ml^2\sin\theta(\sin\theta-\mu_k \cos \theta)}$$ I have managed to solve this equation using DSolve. Now, I want to substitute the solution $\theta [t]$ into another function: $$F[t]=m[l(\ddot\theta \cos \theta-\dot\theta^2 \sin\theta)]$$. However, I cannot do it.
The code is attached:
sol=DSolve[θ''[t]==(m l (g - Ι (θ'[t])^2 Cos[θ[t]])(Sin [θ[t]]-μk Cos[θ[t]]))/(Ι + m l^2 Sin[θ[t]](Sin[θ[t]]-μk Cos[θ[t]])), θ[t], t]
Ak = sol[[1]]
j = sol[[2]]
DSolve [{F[t] ==m l (θ''[t] Cos[θ[t]]-θ[t]'^2 Sin[θ[t]])}/.k,F[t],t]
DSolve [{F[t] ==m l (θ''[t] Cos[θ[t]]-θ[t]'^2 Sin[θ[t]])}/.j,F[t],t]
DSolve[{n[t]- m g==-m l(θ''[t]Sin[θ[t]]+θ'^2 Cos[θ[t]]) }/.k, n[t], t]
DSolve[{n[t]- m g==-m l(θ''[t] Sin[θ[t]]+θ'^2 Cos[θ[t]]) }/.j, n[t], t]
m=0.03517;
l=0.0279;
g=9.81;
Ι=10^-3;
μk=0.1827;
DEFricitonk = NDSolve[{F[t] ==m l (θ''[t] Cos[θ[t]]-θ[t]'^2 Sin[θ[t]]), θ[0]== π/2,θ'[0]==0, F[0]==0}/.k,F,{t,0,5}]
DEFrictionj= NDSolve[{F[t] ==m l (θ''[t] Cos[θ[t]]-θ[t]'^2 Sin[θ[t]]), θ[0]== π/2,θ'[0]==0, F[0]==0}/.j,F,{t,0,5}]
DENormalk= NDSolve[{n[t]- m g==-m l(θ''[t]Sin[θ[t]]+θ'^2 Cos[θ[t]]) , θ[0]== π/2,θ'[0]==0, F[0]==0}/.k,n,{t,0,5}]
DENormalj= NDSolve[{n[t]- m g==-m l(θ''[t]Sin[θ[t]]+θ'^2 Cos[θ[t]]) , θ[0]== π/2,θ'[0]==0, F[0]==0}/.j,n,{t,0,5}]
Please send help. Thank you so much.
DSolveValue
orNDSolveValue
might give answers in a more convenient form for you. $\endgroup$