Well t is in fact time and \dot{t} is the derivative of t with respect to u (the curve along which the integration takes place).
Thanks for your answer - it's all clear now...
Thanks for that, that helps.
But just to explore this a bit.
The first term for the Lagrangian is the below.
g_{\beta\gamma}\dot{x}^{\beta}\dot{x}^{\gamma}
I can imagine writing this out explicity as a big sum in which case there may well be instances of x^alpha in the sum, in which...
Thanks for that, that helps.
But just to explore this a bit.
The first term for the Lagrangian is the below.
\frac{\partial L}{\partial x^{\alpha}}- \frac{d}{du} \left( \frac{\partial L}{\partial \dot{x}^{\alpha}} \right)=0
(g_{\beta \gamma}\dot{x}^{\beta}\dot{x}^{\gamma})
I can imagine...
Cheers for that. I'll change the layout tonight. Any light on my question in the meantime would be appreciated. I'm a banker by day, reminiscing my background of physics, contemplating a move back...
Homework Statement
Hi,
I am reading Ray d'Inverno's book, 'Introducing Einstein's Relativity' and there is a particular derivation of the geodesic equation that I get stumped on (chapter 7). It is a variational method and the final equation is
df/dx_alpha-d/du{df/dx_alpha_dot}=0
where...