Abstract
The third chapter covers the first integral and the variational principle. The notions of cyclic coordinates and Poisson brackets are first recalled. The Theorem of Poisson, Euler equation, and the variational principle are then addressed. An application in optics, namely the Fermat principle, is reviewed. Five exercises are then solved, namely on the Watt Regulator, on the first integral of a free material point, on the brachistochrone problem, on the minimum surface of revolution, and on optical paths and Fermat principle.
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- 1.
If this is not the case, the real non-planar trajectory can be broken down into a series of trajectory elements that can be locally approximated by plane trajectory elements in planes tangential to the real trajectory element.
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Pletser, V. (2018). First Integral and Variational Principle. In: Lagrangian and Hamiltonian Analytical Mechanics: Forty Exercises Resolved and Explained. UNITEXT for Physics. Springer, Singapore. https://doi.org/10.1007/978-981-13-3026-1_3
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DOI: https://doi.org/10.1007/978-981-13-3026-1_3
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-13-3026-1
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