Semjon Adlaj

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Semjon Adlaj is a prominent Russian mathematician and physicist, known for applying advanced mathematical methods to fundamental problems of classical mechanics. His results include introducing the MAGM for calculating the length of a thread in a linear parallel force field. His formula

$l=N(k,1/k),$

links the length of a thread in linear parallel repelling force field $l$ with the Jacobi elliptic modulus $k$. The fact that the MAGM can be calculated in two equivalent ways, one of which is mediated via the AGM, allows us to attain an eloquent formula for the perimeter of an ellipse $L$ of an ellipse with semi-axes $a$ and $b$:

$L={\frac {2\pi N(a^{2},b^{2})}{M(a,b)}},$

as well as, a succint formula for $\pi$:

$\pi ={\frac {M({\sqrt {2}})^{2}}{N(2)-1}},$

where $M(x)$ is the AGM of 1 and $x$, and $N(x)$ is the MAGM of 1 and $x$.

Semjon Adlaj attained new efficient formulas for calculating integrals of elliptic functions, based on the Galois elliptic function.

In 2018 he coauthored a paper, where the Galois axis was introduced into rigid body dynamics.

External links

• Semjon Adlaj's home page

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