 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-3/25i/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

d u^{2} + Y (u)^{2} d v^{2},

v

Γ_{uv}^{v} = Γ_{vu}^{v} = \frac{Y ^{'}}{Y} .

Thus a geodesic obeys

\overset{v}{¨} + 2 \frac{Y ^{'}}{Y} \overset{u}{˙} \overset{v}{˙} = 0.

Y^{2}

turns this into

\frac{d}{d t} (Y (u (t))^{2} \overset{v}{˙} (t)) = 0.

Y (u)^{2} \overset{v}{˙} = constant .

It is also the conserved momentum associated with the cyclic coordinate

v

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