- #1
Apashanka
- 429
- 15
if ##d^3x=Jd^3X...(1) ## where ##x's## evolves with time and ##X's## are constt. and ##x_i=f(X_i)##(for ##i^{th}## coordinate) where the functional form of ##f(X_i)## changes with the time evolution of ##x_i##.
Now taking time derivative of (1) and dividing throughout by (1) it is coming ##\dot J=J(\nabla•v)##(##x## and ##X## are coordinates) which is consistent.
But another thing is approximated while doing this ##\frac{d}{dt}(dx_i)=d(\frac{dx_i}{dt})=dv_i## actually I try to prove it by hand but can't...
Will anyone provide me any hints...
Now taking time derivative of (1) and dividing throughout by (1) it is coming ##\dot J=J(\nabla•v)##(##x## and ##X## are coordinates) which is consistent.
But another thing is approximated while doing this ##\frac{d}{dt}(dx_i)=d(\frac{dx_i}{dt})=dv_i## actually I try to prove it by hand but can't...
Will anyone provide me any hints...