Titlebook: Classical and Quantum Dynamics; from Classical Paths Walter Dittrich,Martin Reuter Textbook 19921st edition Springer-Verlag Berlin Heidelbe

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Action-Angle Variables,necessarily . = α.. But the . are, like the α., constants. On the other hand, . develops linear with time: . with constants . = .(.) and β.. The transformation equations which are associated with the above canonical transformation generated by .(., .) are given by

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The Action Principles in Mechanics,.. , ., are points in .-dimensional configuration space. Thus .(.) describes the motion of the system, and . determines its velocity along the path in configuration space. The endpoints of the trajectory are given by .(.) = ., and .(.) = ..

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Jacobi Fields, Conjugate Points,particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points . and . by ?, then Jacobi’s princi

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Action-Angle Variables, .) is the generator of a canonical transformation to new constant momenta . (all . are ignorable), and the new Hamiltonian depends only on the .: . = . = .(.). Besides, the following canonical equations are valid: . The . are . independent functions of the . integration constants α., i.e., are not

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