- #1
Luke Tan
- 29
- 2
In his book, Landau mentioned varying the relativistic lagrangian
However, I do not understand how he got from varying the integral of ds to varying only the contravariant components.
Would the general procedure not be varying
$$\delta S = -mc\delta\int_a^b\frac{dx_idx^i}{\sqrt{ds}}$$ and then expanding using the quotient & chain rule?
Why is the ##\delta## now appearing only on the $$dx^i$$?
Any help would be appreciated
Thanks!
However, I do not understand how he got from varying the integral of ds to varying only the contravariant components.
Would the general procedure not be varying
$$\delta S = -mc\delta\int_a^b\frac{dx_idx^i}{\sqrt{ds}}$$ and then expanding using the quotient & chain rule?
Why is the ##\delta## now appearing only on the $$dx^i$$?
Any help would be appreciated
Thanks!