Skew-Symmetric Lax Polynomial Matrices and Integrable Rigid Body Systems

Skew-symmetric matrix Lax polynomials are considered. Few rigid body systems with such representations are presented. Lagrange bitop is completely integrable four-dimensional rigid body system. Algebro-geometric integration procedure, using Lax representation, for that system is performed. This integration is based on deep facts from the theory of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. Class of isoholomorphic integrable systems is established and importation class of its perturbations is observed, generalizing classical Hess-Appel'rot system.