Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2019-06-15 02:39:37

Jaspers
Member
Registered: 2019-05-24
Posts: 54

Geodesics

A geodesic on a smooth manifold M with an affine connection ∇ is defined as a curve γ(t) such that parallel transport along the curve preserves the tangent vector to the curve, i.e.

at each point along the curve, where

is the derivative with respect to t.

Using local coordinates on M, we can write the geodesic equation (using the summation convention) as the ordinary differential equation

where

are the coordinates of the curve γ(t) and

are the Christoffel symbols of the connection ∇.


[Source: Wikipedia]


Reason is like an open secret that can become known to anyone at any time; it is the quiet space into which everyone can enter through his own thought.

Offline

Board footer

Powered by FluxBB