Geodesics on Cylinders and Surfaces of Revolution

Описание к видео Geodesics on Cylinders and Surfaces of Revolution

We have previously found the system of nonlinear second order differential equations which must be satisfied in order for a curve to be a geodesic (   • The Geodesic Equation  ). We find what these equations are on a cylinder, and show that helices are geodesics. We then consider the geodesic equations for general surfaces of revolution. The resulting equations are nonlinear and depend on the parameterization of the curve that you are rotating, so there is no general formula for a solution. We do observe that meridians will be geodesics.

#mikethemathematician, #mikedabkowski, #profdabkowski, #tensoranalysis, #geodesic

Комментарии

Информация по комментариям в разработке

Похожие видео