Geodesic Deviation & Jacobi Fields

The Jacobi equation D²J/ds² + R(J,T)T = 0 governs how nearby geodesics separate. On a sphere (K>0) they converge; on a saddle (K<0) they diverge exponentially; flat space gives parallel lines.

Curvature K: 1.0

Initial separation ε: 0.15

Geodesic speed v: 1.0

Curvature K—

J(s) at s=π/2—

Surface type—

Conjugate point s—