A large number of particles, each of mass (m), move in response to a uniform gravitational field

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A large number of particles, each of mass \(m\), move in response to a uniform gravitational field \(g\) in the negative \(z\) direction. At time \(t=0\), they are all located within the corners of a rectangle in \(\left(z, p_{z}\right)\) phase space, whose positions are: (1) \(z=z_{0}, p_{z}=p_{0}\), (2) \(z=z_{0}+\Delta z, p_{z}=p_{0}\), (3) \(z=z_{0}, p_{z}=p_{0}+\Delta p\), and (4) \(z=z_{0}+\Delta z, p_{z}=p_{0}+\Delta p\). By direct computation, find the area in phase space enclosed by these particles at times 

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Also show the shape of the region in phase space for cases (b) and (c).

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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