Shortest Path Between Two Points On A Sphere
Using the Euler-Lagrange Equation to show that the shortest distance path between two points on a sphere is the arc of a great circle.
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File:Illustration of great-circle distance.svg
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CHAPTERS:
0:00 Intro
1:40 Kinematics
2:44 Incremental Distance
7:15 The Distance Between Two Points
8:28 The Functional
9:55 The Form of the Euler-Lagrange Equation
11:24 Substitution into the E-L Equation
13:35 Integrating φ'
20:15 Equation of a Plane
22:23 Arc of a Great Circle
25:09 Recap
26:16 Outro