Brachistochrone Articles

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Brachistochrone

Explaining the General Brachistochrone Problem

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Consider a problem about the curve of fastest descent in the following generalized statement. Suppose that we have a Lagrangian system $$L(x,\dot x)=\frac{1}{2}g_{ij}(x)\dot…
subway

Brachistochrone Subway Tunnels: Speed vs. Depth Tradeoffs

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Introduction A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train would…