Classical Mechanics

Brachistochrone Problem

Question If a particle falls from rest under the influence of gravity from higher to lower point in the minimum time, what is the curve that the particle will follow? Solution Suppose v is the speed of the particle along the curve, then in traversing ds portion of the curve time spent would be

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Lorentz Transformation

Derivation of Lorentz transformation equations using orthogonal transformations Let us consider two uniformly moving frames of reference where origins coincides at $t=0$. let the source of light is fixed at unprimed frame of reference and emits a pulse of light. The observer fixed in the unprimed frame of reference will observe a spherical wave-front propagating

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