Formula:7869

Digital Library of Mathematical Functions ID 22.19.E2

${\displaystyle{\displaystyle\sin\left(\tfrac{1}{2}\theta(t)\right)=\sin\left(\frac{1}{2}\alpha\right)\operatorname{sn}\left(t+K,\sin\left(\tfrac{1}{2}\alpha\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle\theta(t)}}$: angular displacement
• ${\displaystyle{\displaystyle\alpha}}$: initial displacement
 

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