Thanks, I thought about the same process but was unsure of its veracity, guess I‘ll try to work in my system with the idea of energy dissipation term. Thank you very much for your answer.
The integral is this one:
##\int (\dot x)^2 \, dt,##
With ##x=x(t). ##
I don't know how to solve that integral and I haven't find nothing to read about on how to proceed with this kind of (implicit function?) integrals without having the initial function.
The integral is (dx/dt)^2 dt, where x=x(t) so it can't be just x + C.
The non linear system for whom wants to know how did I get to that point is:
d(dx/dt)/dt = sqrt(a^2+b^2)*sin(x+alfa+phi) - Kd*(dx/dt); where alfa = atan(a/b), phi = constant angle, Kd = constant coefficient.
After...