The Geodesic Equation скачать в хорошем качестве

The Geodesic Equation

We consider the length of a curve on a manifold, which is the integral between two times of the square root of the invariant ds^2 = g_{ij} dx^i dx^j. When we wish to minimize this expression over all curves that go through two points, we employ the Euler-Lagrange Equations (   • The Euler-Lagrange Equations  ). Using properties of the derivative of the metric tensor, we arrive at a system of second order nonlinear differential equations known as the geodesic equations. #mikethemathematician, #mikedabkowski, #profdabkowski, #tensoranalysis, #geodesic