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106 views

Lagrange multipliers for finding geodesics on a sphere

The problem statement, all variables and given/known data Find the geodesics on a sphere $g(x,y,z)=x^{2}+y^{2}+z^{2}−1=0$ arc-length element $ds=\sqrt{dx^{2}+dy^{2}+dz^{2}}$ Relevant equations ...
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453 views

Solving geodesic problems with Euler-Lagrange equation

This is the question: Problem B.1 Two cities - Tel-Aviv, Israel and SanDiego, CA - have the same latitude 32 ◦ N, but, different longitudes: Tel-Aviv is 34 ◦ E and San-Diego is 117 ◦ W. What is the ...