A hemispherical bowl of radius a is held fixed with its rim upwards and horizontal. A particle of mass m moves without friction on its inner surface while being subject to the gravitational force -mg (see figure). (a) Find the Lagrangian of the system in terms of spherical polar coordinates. (b) Derive the corresponding equations of motion using the Euler-Lagrange formulation. (c) Show that it is possible to have circular orbits with 6 00, a constant. Find an equation of 00 in terms of m, g, a and a constant of motion.

A hemispherical bowl of radius a is held fixed with its rim upwards and horizontal. A particle of mass m moves without friction on its inner surface while being subject to the gravitational force -mg (see figure). (a) Find the Lagrangian of the system in terms of spherical polar coordinates. (b) Derive the corresponding equations of motion using the Euler-Lagrange formulation. (c) Show that it is possible to have circular orbits with 6 00, a constant. Find an equation of 00 in terms of m, g, a and a constant of motion.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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