The geometric formula of self sustaining Hamiltonian mechanics within the phrases of symplectic and Poisson manifolds is usually authorized. The literature in this topic is broad. the current booklet presents the geometric formula of non-autonomous mechanics in a common surroundings of time-dependent coordinate and reference body changes. This formula of mechanics as like as that of classical box concept lies within the framework of common concept of dynamic platforms, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will discover a strict mathematical exposition of non-autonomous dynamic platforms, Lagrangian and Hamiltonian non-relativistic mechanics, relativistic mechanics, quantum non-autonomous mechanics, including a few complex versions - superintegrable structures, non-autonomous limited structures, concept of Jacobi fields, mechanical platforms with time-dependent parameters, non-adiabatic Berry section conception, instantwise quantization, and quantization relative to various reference frames.
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