Sonya Kovalevsky’s Work on

The Rotation of a Solid Body about a Fixed Point


By April Lail and Emily Anthony

 

 


Sonya Kovalevsky

1850-1891

 

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 Joseph-Louis 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 y-axis.

Here is an example of one of these types of tops (best viewed in Internet Explorer, which correctly lines up the arrows with the appropriate places on the top).


 

Animated GIF Created by Webpromotion, Inc.  

 


Center of mass on

The y-axis, 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 y-axis.

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 y-axis either.

(hint:  weight one side of the top)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Kovalevsky Crossword - BEST VIEWED IN INTERNET EXPLORER

 


1

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.”  Springer-Verlag, 1978.

 

2.     Rappaport, Karen D.  “S. Kovalevsky: A Mathematical Lesson.”  The American

Mathematical Monthly 88 (October 1981):  564-573.

 

3.     The Works of Sonya Kovalevskaya web page, by Kimberly A. Meares,

http://home8swipnet.se/~w-80790/Works/Kovalevs.htm