Theorem In Classical Mechanics Research Articles

Noether’s theorem in classical mechanics

A simple statement of Noether’s theorem as it applies to classical mechanics is given and proved. It is then used to generate constants of the motion associated with Lagrangians possessing certain transformation properties.

Noether's theorem for optimum control systems

Abstract In this paper Noether's theorem of classical mechanics and the variational calculus is developed for optimum control systems. Also, it is shown that the existence of first integrals of Pontryagin's maximum principle equations depend on the existence of solutions of a system of partial differential equations—generalized Killing's equations —for optimum control systems.

Geometric wave propagation through curved media

Application of the laws of geometric optics to curved media presents few additional complications. The invariance of the wave-vector density of a wave grouplet, as deduced from Liouville's theorem in classical mechanics, is also true for curved media. The equations governing the spatial and time variation of wave spectra and ray paths on curved surfaces are developed.

A Conservation Theorem in Classical Mechanics

First Page