An integrable system with a nonintegrable constraint. (English) Zbl 1113.37059
Math. Notes 80, No. 1, 127-130 (2006); translation from Mat. Zametki 80, No. 1, 131-134 (2006).
From the introduction: We show that there exists an invariant measure for a disk sliding on an icy sphere in the gravity field if the disk’s center of mass lies at an arbitrary point of the axis perpendicular to the plane of the disk and passing through the disk’s center. This results in the zero measure of the set of fall trajectories. For inertial motion, the problem is integrable, and we manage to obtain a solution in quadratures.
MSC:
| 37N05 | Dynamical systems in classical and celestial mechanics |
| 70F10 | \(n\)-body problems |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
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