Spherical Pendulum
978-613-1-19044-5
6131190445
144
2010-11-17
45.00 €
eng
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Spherical pendulum is a generalization of the pendulum. It consists of a mass moving without friction on a sphere. The only forces acting on the mass are the reaction from the sphere and gravity. It is convenient to use spherical coordinates and describe the position of the mass in terms of (r,θ,φ), where r is fixed. The Lagrangian is L=frac{1}{2} mr^2left( dot{theta}^2+sin^2theta dot{phi}^2 right) + mgrcostheta. The Euler-Lagrange equations give frac{d}{dt} left(mr^2dot{theta} right) -mr^2sinthetacosthetadot{phi}^2+ mgrsintheta =0 and frac{d}{dt} left( mr^2sin^2theta , dot{phi} right) =0 showing that angular momentum is conserved.
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