Kovalevskaya's integrable case: generalizations and related new results (Q1876377)

More than 11 decades have elapsed since \textit{S. V. Kovalevskaya} discovered her famous case of integrability of the equations of motion of a heavy rigid body about a fixed point [Acta Math. 12, 177--232 (1889; JFM 21.0935.01)]. Nevertheless, the last 17 years have witnessed the emergence of some amazing and even unexpected results generalizing this case or valid under the same condition \(A=B=2C\). In this paper the author gives a summary of known integrable cases of Kovalevskaya's type and points out some of their generalizations. A total of four general and five conditional integrable cases is listed. Of those, two general and three conditional cases are introduced for the first time.