Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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What are some practical applications of Lagrange's equations in the field of physics?
A frictionless table has a mass m on it. The table has a hole in it, where mass m is connected to a string that passes through the hole, attached to a hanging mass M.(a) What is the Lagrangian for this system? Using this Lagrangian, find the equations of motion (a = function of position) for each of the generalized coordinates used.(b) Under what conditions does m make a circular motion?(c) What is the frequency of small oscillations (in r) about this circular motion? Further, assume the oscillations are small: use a Taylor Expansion at the point we choose to use the small angle approximation.)
Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius8​units, with linear speed 3units per second.
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Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning