Find the geodesics on the surface of a sphere of radius a by:
(a) writing the geodesic equations for the spherical coordinates given by:
x = rsinTcosP
y = rsinTsinP
z = rcosT
for T and P(the r - equation can be ignored as a = constant);
(b) exhibit a particular solution of these two equations; and (c) generalize (b).
Geodesic equation in general form (sorry don't know how to use LaTeX)
The Attempt at a Solution
Ok so I did part (a) and ended up with the equations for T and P as follows:
d^2T / ds^2 - (sinTcosT) * (dP / ds)^2 = 0
d^2P / ds^2 - 2cotT * (dT / ds) * (dP / ds) = 0
I am terrible at solving differential equations and basically have no idea what to do from here to find a particular solution. I was hoping someone could guide me through it.