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Fermat's principle * * Wikipedia: *In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light. However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary optical length. Fermat's principle can be used to describe the properties of light rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It follows mathematically from Huygens' principle (at the limit of small wavelength), and can be used to derive Snell's law of refraction and the law of reflection.*908

Gauss' principle of least constraint * * Wikipedia: *The principle of least constraint is a least squares principle stating that the true motion of a mechanical system of N masses is the minimum of the quantity above for all trajectories satisfying any imposed constraints, where m-k, r-k and F-k represent the mass, position and applied forces of the kth mass. Gauss' principle is equivalent to D'Alembert's principle. The principle of least constraint is qualitatively similar to Hamilton's principle, which states that the true path taken by a mechanical system is an extremum of the action. However, Gauss' principle is a true (local) minimal principle, whereas the other is an extremal principle.*904

Principle of least action * * Wikipedia: *In physics, the principle of least action - or, more accurately, the principle of stationary action - is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. The principle led to the development of the Lagrangian and Hamiltonian formulations of classical mechanics. ... Maupertuis felt that "Nature is thrifty in all its actions" ... the action principle is not localized to a point; rather, it involves integrals over an interval of time and (for fields) an extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., Given that the particle begins at position x1 at time t1 and ends at position x2 at time t2, the physical trajectory that connects these two endpoints is an extremum of the action integral. In particular, the fixing of the final state appears to give the action principle a teleological character which has been controversial historically.*903

Scientific method | ||||

Scientific method Physics experiments | ||||

Hypothesis | ||||

Hypothesis Mapping observables and observations | ||||

Experimental design | ||||

Experimental design Design experiments to rule models in or out Conservation of linear momentum Conservation of probability density CPT symmetry Noether's Theorem | ||||

Experiments and Theory | ||||

Experiments and Theory Thought experiments in Physics Brownian ratchet Einstein's box |