LagrangeEuler
- 711
- 22
If we have system of 3 ordinary differential equation in mechanics and we have two initial condition ##\vec{r}(t=0)=0## and ##\vec{v}(t=0)=\vec{v}_0 \vec{i}##. If we somehow get
\frac{d^2v_x}{dt^2}=-\omega^2v_x
then v_x(t)=A\sin(\omega t)+B\cos(\omega t)
Two integration constants and one initial condition for velocity. What to do? Should we put that one constant is equal to zero? So ##A=0##, ##B=v_0##?
\frac{d^2v_x}{dt^2}=-\omega^2v_x
then v_x(t)=A\sin(\omega t)+B\cos(\omega t)
Two integration constants and one initial condition for velocity. What to do? Should we put that one constant is equal to zero? So ##A=0##, ##B=v_0##?