Titlebook: Classical and Quantum Dynamics; From Classical Paths Walter Dittrich,Martin Reuter Textbook 2020Latest edition The Editor(s) (if applicable

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Kristin L. Huffman,Andrea Giordanors appear in the expression for the adiabatic invariants. We now wish to begin to locally remove such resonances by trying, with the help of a canonical transformation, to go to a coordinate system which rotates with the resonant frequency.

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Sander Münster,Aaron Pattee,Florian Nieblingo-dimensional surface. If we then consider the trajectory in phase space, we are interested primarily in its piercing points through this surface. This piercing can occur repeatedly in the same direction. If the motion of the trajectory is determined by the Hamiltonian equations, then the . + 1-th piercing point depends only on the .th.

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https://doi.org/10.1007/978-3-642-16370-8The subject of this monograph is classical and quantum dynamics. We are fully aware that this combination is somewhat unusual, for history has taught us convincingly that these two subjects are founded on totally different concepts; a smooth transition between them has so far never been made and probably never will.

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https://doi.org/10.1007/978-3-642-16370-8We begin this chapter with the definition of the action functional as time integral over the Lagrangian . of a dynamical system: . Here, .., . = 1, 2, …, ., are points in .-dimensional configuration space.

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,Micromouse – Electronics on Wheels,We begin this chapter by deriving a few laws of nonconservation in mechanics. To this end we first consider the change of the action under rigid space translation .. = .. and .(..) = 0.

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A Mobile Robot for EUROBOT Mars Challenge,Let .., .., …, .., ....., ….. be 2. independent canonical variables, which satisfy Hamilton’s equations: . We now transform to a new set of 2. coordinates .., ….., .., ….., which can be expressed as functions of the old coordinates:

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