- #1
latentcorpse
- 1,444
- 0
I have two equations:
[itex]\ddot{x}^\mu + \ddot{y}^\mu + \Gamma^\mu{}_{\nu \lambda} (x+y)(\dot{x}^\nu+\dot{y}^\nu)(\dot{x}^\lambda+\dot{y}^\lambda)=0[/itex]
and
[itex]\ddot{x}^\mu + \Gamma^\mu{}_{\nu\lambda}(x) \dot{x}^\nu \dot{x}^\lambda=0[/itex]
apparently if i taylor expand the first equation to first order and then subtract the second equation i should get
[itex]\ddot{y}^\mu + \frac{\partial \Gamma^\mu{}_{\nu\lambda}}{\partial x^\rho} \dot{x}^\nu \dot{x}^\lambda y^\rho = 0 [/itex]
i cannot show this. how do we go about taylor expanding something like that?
[itex]\ddot{x}^\mu + \ddot{y}^\mu + \Gamma^\mu{}_{\nu \lambda} (x+y)(\dot{x}^\nu+\dot{y}^\nu)(\dot{x}^\lambda+\dot{y}^\lambda)=0[/itex]
and
[itex]\ddot{x}^\mu + \Gamma^\mu{}_{\nu\lambda}(x) \dot{x}^\nu \dot{x}^\lambda=0[/itex]
apparently if i taylor expand the first equation to first order and then subtract the second equation i should get
[itex]\ddot{y}^\mu + \frac{\partial \Gamma^\mu{}_{\nu\lambda}}{\partial x^\rho} \dot{x}^\nu \dot{x}^\lambda y^\rho = 0 [/itex]
i cannot show this. how do we go about taylor expanding something like that?