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Final Lagrangian

The Lagrangian of our system is therefore:

L=ms˙22−GMm[(rsummit−∫0ssin⁡θ(σ)dσ)−1−rsummit−1].\begin{aligned} L &= \dfrac{m\dot{s}^2}{2} - GMm\left[\left(r_{\mathrm{summit}} - \int_0^s \sin{\theta(\sigma)}d\sigma\right)^{-1}-r_{\mathrm{summit}}^{-1}\right]. \end{aligned}
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Last modified: October 23, 2026.