Sonya
Kovalevsky’s Work on
The
Rotation of a Solid Body about a Fixed Point
By April Lail and
Emily Anthony
Sonya
Kovalevsky
18501891
Sonya Kovalevsky was the
first woman to receive a Ph.D. in mathematics. Her work consists of ten papers in mathematics and
mathematical physics, including topics such as the theory of partial
differential equations, abelian integrals, and the propagation of light in
crystals. Her mot noted work is on
the problem of the rotation of a rigid body about a fixed point [1 and 3]. It was for this that Sonya was awarded
the Prix Bordin of the French Academy of Sciences in 1888 [1].
Although
Kovalvesky achieved monumental success, this did not mean she did not encounter
many obstacles. As a female in the
late 1800s, Sonya struggled to be accepted as an equal to her male
counterparts. Sonya was repeatedly
denied an education: first by her
father and then by several universities.
As a result of her experiences, Sonya was determined to prevent others
from the same hardships. She used
her reputation to assist other Russian women in attending a university [1].
Rotation of a
Solid Body About a Fixed Point
Sonya Kovalevsky is most
famous for her work on the rotation of a rigid body about a fixed point. Using partial differential equations,
Kovalevsky was able to explore the motion of a special type of rigid body. Another way to think about a rotating
solid body is to look at a spinning top.
Throughout history, mathematicians have considered several different
cases of spinning tops.
One
case was explored by JosephLouis Lagrange in 1788. His model can be thought of as a top where the center of
mass of the top is at the center of the top. In his case, the center of mass is also on the axis of
rotation, the yaxis.
Center of mass on
The yaxis, the axis
of rotation
Fixed Point
Another model was
researched by Leonard Euler in the mid to late 1700s. In his model, the center of mass of the body was not in the
center of the top like Lagrange, but at the fixed point where the top
rotated. Once again, the axis of
rotation was the yaxis.
2.
Think
of a way to draw a top where the center of gravity is at the fixed point.
Sonya Kovalevsky’s research centered on
the third case of the rotation of a solid body about a fixed point. In her model, Sonya considered
weighting the top so that it was no longer symmetrical [2]. In other words, the center of mass of
the top was no longer on the axis of rotation.
3.
Once
again, try to draw a top with the center of mass not at the
center
of the top, but this time, draw the top
so
that the center of mass is not on the yaxis either.
(hint: weight one side of the top)
Kovalevsky
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Down:
2. Sonya was born in
____, Russia.
3. Sonya was tutored by
Karl _____.
4. The mathematician
awarded the Prix Bordin in 1888 was _______.
5. Sonya’s research
focused on the rotation of a ________ body.
8. Sonya died of ______
in 1891.
Word Bank
Prix Bordin Vladimir
Solid Calculus Moscow
Sine Pneumonia
Weierstrass Stockholm
Sonya Kovalevsky
Across:
1. Sonya was a professor at the University
of _______.
4. To learn Physics, Sonya taught herself
the _____ function.
6.
In 1888, the French Academy of
Sciences awarded Sonya the _________.
7. ______Kovalevsky
was a “ficticious” husband.
9. These notes were on
Sonya’s nursery walls.
References
1. Kovalevsky, Sofia. “A Russian Childhood.” SpringerVerlag, 1978.
2. Rappaport, Karen D. “S. Kovalevsky: A Mathematical
Lesson.” The American
Mathematical Monthly 88
(October 1981): 564573.
3. The Works of Sonya
Kovalevskaya web page, by Kimberly A. Meares,
http://home8swipnet.se/~w80790/Works/Kovalevs.htm