Geodesics on Curved Surfaces
Shortest paths bent by curvature — Euler-Lagrange equations in action
Sphere
Torus
Saddle
Initial angle θ₀
30°
Latitude start φ
30°
Path length
300
Rotation speed
40
Geodesics are solutions to the Euler-Lagrange equations — extremals of arc-length functional ∫√(gᵢⱼ ẋⁱẋʲ) dt