- #1

WannabeNewton

Science Advisor

- 5,800

- 532

## Homework Statement

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).

## Homework Equations

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.