Scientific and teaching activities of I. I. Somov

Iosif (Osip) Ivanovich Somov (1815-1876) was graduated from Physics and Mathematics Faculty of Moscow University in 1835. He was awarded a candidate degree. Before 1841, he taught mathematics in the Moscow Commercial School and the Nobility Institute. He defended a Master thesis in the same year and started teaching at St. Petersburg University.
I. I. Somov's area of interest was very vast: geometry, mathematical physics, higher algebra, calculus and elliptic functions, and analytic mechanics. He was three times awarded the Demidov Prize. Somov was elected a corresponding member of the Emperor’s St. Petersburg Academy of Sciences in 1852. In 1862, he was elected an ordinary academician.
The legacy of I. I. Somov includes highly interesting work Algebraic Equation to Determine Small Oscillations of System of Material Points (1859), where he proved that frequency equation can have multiple roots. In contrary to Lagrange's (1736-1813) opinion, it does not lead to incorporation of time variable outside sine and cosine functions in solution of small oscillations differential equation. This result was obtained simultaneously with K. Weierstrass (1815-1897). It was critical for the understanding of properties of characteristic equation roots.
As to I. I. Somov's educational materials, we shall mention his innovative course Rational Mechanics. Its first part was titled Kinematics and was published in 1872. The second part Introduction in Statics and Dynamics and Statics was published in 1877 after his death. His original results on high-order accelerations theory, attraction theory, and dynamics of a rigid body with one fixed point complemented the course of Rational Mechanics. It was the first course in Russia where kinematics was explained in terms of vector calculus. I. I. Somov used curvilinear coordinates, which was also new. Rational Mechanics was recognized in Europe. This course was published in Germany in 1878.