Particle on Curved Surface under no Force moves along Geodesic

Theorem

Consider a particle $P$ which is constrained to move on a curved surface $C$.

Let $P$ be such that no force acts upon it.

Then $P$ moves along a geodesic.

Proof

This theorem requires a proof. In particular: A consequence of Hamilton's Principle in the calculus of variations. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.32$: Riemann ($\text {1826}$ – $\text {1866}$)